I interrupted this program that they're having that the Congress has on UNRWA. An organization that's critical for Palestinian survival in Gaza. Critical for that, the health, the education, the medical care. Easy, easy, I really bruise, I bruise. I've been to Gaza 10 different times. I've been there to see the destruction at earlier times when the Israelis were killing people. It's just terrible what's going on right now. 26,000 people that have been killed. Kids that have been killed. All of these people that are undergoing, you know, invitations with no medicine. Anesthesia, nothing. And then the starving, these kids that are starving to death. That there's no food that they're not letting the food in. And then the Biden administration. I mean we're dealing with weapons, we're killing them with weapons, we're killing them with weapons.


Bismillahirrahmanirrahim. So I actually wanted to start with an ayah, and this is ayah 36 in Surah Yasin. Glory be to the One who created pairs from everything, created all of the pairs from what comes out of the earth from themselves and from what they don't know. Because I feel like sometimes we ask this question, what is the wisdom in creating humanity into like these buckets? Like why?   The existence of men and women on earth, whether we acknowledge it or not, is honoring Allah Subhanahu Wa Ta'ala's oneness, Allah Subhanahu Wa Ta'ala's power. Am I doing this wrong? Can you hear me now? What was the sprint commercial? And this is why Allah Subhanahu Wa Ta'ala in Surah An-Najm says Allah Subhanahu Wa Ta'ala, one of the testiners of who he is, Subhanahu Wa Ta'ala, I just want to pause.  Allah Subhanahu Wa Ta'ala is beyond gender, is beyond needing us, hence the oneness of Allah Subhanahu Wa Ta'ala. The word Allah in Arabic literally means the one and only God. It's a word that inherently cannot be pluralized. Subhanallah. So incredible. But I want to talk about this, so I wanted to talk a little bit about the theory, the current situation that we're in, and then hopefully the remedies from our tradition. So the theory makes a lot of sense. Like in a number of places in the Quran Allah Subhanahu Wa Ta'ala says And whoever does good deeds, male or female. Sometimes it says, But over and over again, when Allah Subhanahu Wa Ta'ala mentions male and female, mentions them together and says whoever does good deeds. Again, the focus on the action. Whoever is actually doing these actions, they are equal in the eyes of Allah Subhanahu Wa Ta'ala. Hence the discussion on equality.  And then she has a daughter and she says She's like, Ya Allah, it's a girl. Allah knows what, it's not like Allah didn't know it was a girl. And it says And the male is not like the female. And I feel like there's a beautiful subtlety in that, because as we aspire, we don't aspire for equality in the sense of we're exactly the same, we aspire for equity. And I know it's a subtle difference, but it actually makes a lot of sense. Because if we set men as the standard, it's an inherently losing proposition for women to always try to aspire to be men. I don't want to be a man. Alhamdulillah, I'm very happy being a woman. I don't want to be a man. But also in that moment, Sayyidina Maryam A.S. is such a beautiful example that her mother, she filled a role that only a woman could. And prepared her community for a role that Sayyidina Maryam A.S. would later take on. She was part of that journey. Alhamdulillah. I just think it's so beautiful when you talk about her. I'm just like drowning in all of the things that were said before. When we talk about patriarchy, if I say patriarchy is a hierarchy where I'm holding one group above the other. Allah's Panathana is just. Is it just to create half of humanity inherently subservient to the other? Or is there actually a balance? And Allah's Panathana made us a people of balance. And I want to point out that this lack of balance is not just destructive to women, it's also destructive to men.  Most stars are actually two star pairs that are rotating around each other and they're balancing each other out. You know that game where you hold hands and you go really fast in a circle? If it's an adult and a child, the child is flying. And if you're balanced, you're just going around in a circle. That lack of balance is inherently destructive to both groups. And I want to point this out. In American society, single men usually don't get touched. Like don't get hugged, don't get any kind of physical affection unless if they are in a sexual relationship. How destructive is that to people's psyche? But also how destructive is that for our society that the only outlet they have is a sexual relationship? I'm saying this to say that this isn't just bad for the women, it's also bad for the men. The examples of women during the time of the Prophet's life setup are so endless. And Mashallah, we heard so many of them. I wanted to, subhanAllah, in Mecca, Mecca was a lot more patriarchal because it was based on who got to travel and trade. It was dangerous to trade. The men held all of the power, had all of the political power and the financial power. This is why financial literacy for women is so important, because it balances things out. When they got to Medina, they were people that would, they were farmers and the family would farm together. It was a far more balanced society. It's no surprise that Mecca kicked the Prophet's life out and Medina took him in. That's not a coincidence. And subhanAllah, he arrives in Medina and you can see the cultural shift. SubhanAllah, there's a moment where Umar al-Du'l-Lan told him, he's like, remember when we were in Mecca and we would talk and the women would listen and now we can't get a word in edgewise. Like, what happened to us? He's like, I'm like, his brain's melting. He's like, I don't know what to do with this. It's funny because his wife talks back to him. He's like, wait, what's happening? This is new, what's happening? When she tells him you're not better than the Prophet's life, your daughter talks back to him. And he's like, it's a brain melt. He runs stops. He's like, what are you doing? Just like, we all do that. It's not just me. SubhanAllah, this was the norm. This was the standard. He's saying this to the Prophet's life. It was actually a time where the Prophet's life was really upset. And as soon as he said that, he pulled the Prophet's life out of being upset because he couldn't stop laughing. It's like, yes, but... SubhanAllah, that balance is so beautiful. There was a battle called the Battle of Mu'tah. The Muslims went. There were 3,000 of them. They were fighting the Byzantine Empire. They were fighting like 100,000. It was such an intense battle. SubhanAllah, this is right after Khadim, when he becomes Muslim. They engineer this way to like safely retreat. They run back to Medina. And they're on the outskirts of Medina. And the women of Medina come out to them because this is the first time in Islamic history that the Muslims have left a battle. The women come out and say, Ya furrar, ya furrar.  You're not allowed home. And the Prophet's life comes out and intervenes. And he says, Balhumul kurrar, balhumul kurrar. There'll be another round. I promise, please let them home. And the Sahama said, we were far more afraid of the women of Medina than we were of the Byzantine Empire. That we were like fighting the day before. Our strength is believing women. This is what made Medina. This is what made the community that took in the Prophet's life. The Prophet's life said, whoever loves the Ansar, the people that took him in in Medina is a believer.  SubhanAllah. This is the weight of the women in our tradition. And stories like this are endless. I want to talk about part of how we ended up where we are now. So right now, I wanted to actually start off with ussulat al-qasas, because part of the trauma that has happened not just in the Muslim community, but really all over the world was this colonialism. Our grandparents kicked out the colonizers, the military colonizers. There's still economic colonization that's happening all over the world. And colonization is not unknown to this particular piece of land. And at the heart of all of this is white supremacy. Allah SWT, when he's describing the pharaonic system in the Quran and surat al-qasas, the surah is actually called sometimes translated to the stories, but usually translated to the narratives. And it takes the narrative of Pharaoh in one ayah, because it's not even complex, it's like this is it, and then the majority of the surahs are in the story of Sayyidina Musa. But in this ayah, it says, Pharaoh rose in the land, he divided people into groups, and here the word that it's using shia versus ta'ifa, it's a group with a distinct identity. He convinced them they were different from each other. And then he oppressed one of the groups. And the word ta'ifa is just a subgroup. It's actually one group from the many groups. They're not actually different. He kills, and he killed the men, and he kept the women alive. He was one of those people who caused corruption. I think it's important to talk about how the system that we have now is actually specifically gendered and treated men differently from women. And sometimes part of the dichotomies we're seeing in our own Muslim community is because the oppression that we experienced and our parents lived through, the trauma that we experienced communally was different whether you were a man or a woman. I also want to point out that this level of oppression is different based on the other rung of society that Pharaoh divided people into. Based on your race, you might experience more or less of this. But because you're put into this group, everybody's competing to be the model minority. I really don't care if Muslims become the model minority. I care if Muslims actually bring justice. Because that's what we're called to do. And if we work to compete in a system that is oppressing to other people, we're never going to win. Why would we? Why would Allah ever put Barakah in a system where we've just wholesale accepted oppression of other people? And because the Muslims in America are actually the most ethnically diverse religious group in the country, that means that we're not just accepting oppression for other people. We're accepting oppression within our own communities. Why would we ever do that? We're not the point of this. And I also want to point out that when we talk about like this post-colonialist reality that we're all living in, oftentimes you see the same objectification of women that Sadr Hussai spoke about just takes, you know, like this religious veneer we're objectifying women, but now we're like, you should wear a hijab and attract the men. This is my act of worship. How do you make this about you? Like really, how do you make this about you?  If you find women attractive, you lower your gaze. That's your responsibility. In fact, that's my right upon you. I have a right for you to not objectify me. Subhanallah, how can we twist this? You guys have all seen this. It was like for a while it was this horrendous meme. I hated it. There's like a lollipop that's covered and what you guys know what I'm talking about and then there's a lollipop with ants and they're like, this is why you wear hijab and like women are lollipops, men are ants. Like this whole thing is horrendous. But how are you then taking religious language to do exactly the same system of oppression to try to cover up Pharaoh's system to cover up the white supremacist system? Dalim Gahid recently posted this. She said, we look at beauty and we think it's rare. It's not. It's commonplace. When you look into a mirror of like, ya Allah, the same way that you've beautified my outer, beautified my inner. I'm already saying, ya Allah, you've made me beautiful on the outside. And if you're insulting Allah's Pound of Da'ala's creation, where are you insulting? Also, a lot of our beauty standards in our own community are based on white supremacist ideals. I get into this argument so much with Egyptian women. They're like, curly hair is ugly. I'm like, we're North African. Most of us have curly hair.  I'm like, I have a problem. When our colonizer says, I am beautiful and you are not and you say yes. They came around and took down cities that were far more civilized than them and called them savages. The tragedy is when we believe we're actually savages. This isn't us going back. When I'm fighting for women's rights, I had a, I actually recently broke up with my therapist, not to find a new one. But because I was telling her, I'm like, I really care about women's rights. She's like, you clearly have progressive values. I'm like, no, I have very traditional values. Like specifically, 1400 years old. They are very traditional. Thank you. I like that. I have curly hair too. No, but this is true across the board.  Every woman's beautiful. White, black and every shade in between. Again, who are you insulting? Are we really going to go around insulting Allah? His beauty and His creation? What are you doing? Sorry, I know I'm not on this. I feel like we wouldn't be here if there wasn't misogyny in the Muslim community. We actually wouldn't have an audience. I'm sorry. It's important to talk about because I've said this before I've gotten kicked out of more masajid than none because if I go into a masjid and you're like, there's no space for women. I'm like, okay, yell at me when I'm done. Allahu Akbar. Because the prophet of Allah, said, you can't prevent me from being here. The narration that mentioned that Subhan Allah after his father passed away, Abdullah the son of Omar went to his mom and said, why do you keep coming back? And she's like, so what's the reason Omar didn't tell me not to come? He got ashamed and turned away because as her son, if the prophet said them spoke, he doesn't have a right to tell you otherwise. And the irony is like, I remember when COVID first happened and they're like, okay, we'll open the masjid and we'll be socially distanced and we'll do this and we'll do that, but the women shouldn't come because it's not mandatory on them.  Your misogyny is showing. And when they're like, oh no, this isn't about misogyny, this is fiqh. I'm like, okay, so how is the commandment of the prophet that I said I'm not fiqh? How is one statement fiqh and not the other one? When we're talking about these things, I think it's so important that Subhan Allah, we are mindful of this is our tradition. Am I submitting to it or am I trying to fit it in a box? And this is where the root of patriarchy in the Muslim community is. If you accept hierarchy at home, you accept hierarchy in society. And this is why a lot of those those quote, I'm not sure, I'll politely call them opinions. We're often published by the political authority of the time. When you look at the scholars in our own tradition that we're supported by the people, by the way the all of our fiqh, so the four imams, the four medahab, Imam Ja'far al-Sadaq, like when you look at all, and they were all interconnected with each other, they usually had issues with the political authority of the time. Because they understood their role in scholarship is speaking truth to power, is checking power, and historically scholarship was the balance that protected, it was the default senate of like, no, we're gonna check your power in case you ever think you get to oppress the people here. And when you look at those scholars far more balanced, because their role was to maintain society. The foundation of every Muslim society is the family. I also want to say that these extremes that we see in western society is just unfortunately an inherent part of western society. A lot of Islam talks over and over about balance. In western societies we have communism or capitalism or individualism, and you don't have anything in between.  How do I build these balances within our institutions? How do you heal society from the inside out? Again, us showing up as educated, empowered Muslim women, this isn't just for us. This is to bring justice to everyone that is around us. It is to challenge the entire system that said your value is based on white supremacy. It is not a coincidence when you are going to depict Well, I know that Issa didn't have blonde hair and blue eyes. He didn't. But we're going to depict divinity as a white man. That's not a coincidence. And it's an abuse of Christianity. I work with a lot of Christian reverence. By the way, I'm part of an all women's team. I think we're the only one in the country. The rabbis are women, the reverents are women. It's incredible. SubhanAllah, when you talk to them, they're like, Issa didn't look like that. That's not what he looked like. But also, how are you now taking my faith and turning contorting it to something that it's not? We have to have enough life in front of Allah to not be able to tell him. We stood back, watched that happen and said nothing. When we talk about life, let's talk about life in front of Allah. Life is not you sitting in a corner being quiet. All of the women that we learned about, they all had buckets of life. Endless amounts of life. They didn't sit in a corner and be quiet. When someone else was oppressed because they had enough life of Allah to not just take that and not sit back and be quiet. SubhanAllah. How much time do I have? Okay, awesome. Sayyidina Maryam, alaihi salam. Sayyidina Maryam, alaihi salam. When you read her story, we talked a little bit about her, her mom. She's like, Ya Allah, it's a girl. Because she's from Ali Amran, she was able to live within Bayt al-Maqdis, within one of the harems. One of the holiest places on earth. She got to live there and she was the only woman that was allowed to live there. And all she did all day was pray and feed the poor. Like, she was just in a constant state of ibadah. And the angels came to her. And the angels came to her and said, Ya Maryam, oh Maryam, called her out by name. SubhanAllah is so beautiful. You see how Allah, SubhanAllah, calls Maryam, alaihi salam, by name? He calls Sayyidina Musa, alaihi salam, by name. It is to elevate them. And the angels call her by name. Ya Maryam, Allah has chosen you. Oh Maryam. Allah has chosen you. Has purified you. Has chosen you over all of the women. Ya Maryam, O Maryam, be obedient to Allah, SubhanAllah, and make sujud and make ruku'a with those who are making ruku'a. SubhanAllah. This is Maryam, alaihi salam. Allah, SubhanAllah, then gives her a very, very difficult and challenging test. And Jubeel, alaihi salam, comes and he tells her this and he's like, you're gonna have a child. She's like, wait what? And in that moment, as she's about, she's going into labor and she says something that's so profound. She's saying, She said, if only I had died before today and was long forgotten. And I feel like I've read the men who wrote tafasir and they're like, oh, it's because she feared the pain of labor. Like women have had babies and they had more babies. No, that's not what this is. No idea. For someone to say this, there's something inherent and core to who they are that's being threatened. She knew what her people were going to put her through. And mind you, a religious community and what they were going to put her through. As soon as Isa, alaihi salam, is born, he looks up at his mother and he starts to give her, in the qiraat it says, and the one that was below her or from below her, she was called and said, shake the tree. Like be content. And when you meet someone, tell them that you won't speak for three days. When she comes back, carrying Sayyidina Isa, alaihi salam through the city, she's coming back like, mind you, if, I don't know, the woman who basically lives at the masjid and feeds the poor is holding a baby. Maybe she's babysitting. Maybe she found it worth in child. They didn't say any of that. They looked at her because they'd been gearing up to this. They immediately started to slut-shaming her. They told her, your mother was this and your father was this.  Sound familiar?  Also, I don't know how long it takes to go like this. Even as she's doing this, they're like, how can we speak to a child? I, like, subhanallah, the amount of just, she knew this was coming. And as soon as she pointed to him, alaihi salam, he says, I am the servant of Allah. He gave me the book, he made me a prophet. He also says, I am righteous and good to my mother. What I expect of men in our community is to follow in the footsteps of Sayyidna alaihi salam and to be allies to women in this fight. This isn't about like men versus women. This is about justice versus injustice. Are we here for Allah or are we here for power? And everyone gets to decide this. We already talked about how there are certain women that unfortunately uphold some of these horrible systems, like, go, know your place. I actually got an email like that once, which I was like, in my mind, and I'm like, if you were a caricature of a misogynist, you wouldn't have hit it this hard. Sayyidina alaihi salam said, I have my mother's back. And this is what we should expect from the demand of our men. When I first interviewed for the job, Dr. Rani was on the call, I'm like, whatever this job is, I'm taking it. And the first conversation I had, I'm like, oh, I had some really difficult conversations with certain people, and she's like, I'm willing to bet they're the same people. I'm like, I love you so much. It's our responsibility to hold them accountable. And I feel like the more spaces I've been in, there was, I can't even remember his name, and I don't care to mention his name. He came, and he was speaking, and I was working for the Muslim Youth of North America. And he came, and the way he was interacting with the teenage girls didn't, like, it just, it sat with me, and I was like, I don't like this. I don't like what, like, I don't like how you're interacting with them. And I went because I was the one in charge of the list of speakers, and I just took, I just deleted him off, like, a Google Sheet, and I was like, he is not coming back. SubhanAllah, ten years later, I realized that the women took down. And I looked at that, and I was like, SubhanAllah, what if I hadn't trusted my intuition? What if I had sat there and said, oh, but what do I know? And blah, blah, blah, blah. No, the way he was interacting with teenage girls was inappropriate. It is my job to protect them. You have no right to be in this space. If you don't know that you shouldn't be hanging out with teenage girls after hours at a campsite, you should never be allowed to come back.  But I want to stand on the footstep, through the footsteps of Sayyidina Malim A.S. I want to meet her in Jannah and deserve to have a conversation with her. I want to meet Sayyid al-Khawla, R.T. in Jannah. I want to live my life according to those things so I can deserve to be there, so they don't look back at us and say we fought long and hard. What did you do? Sit back and do nothing?  I never, alhamdulillah, I don't... No, I've gotten angry. I'm not going to pretend I haven't. But I remember I walked in, this was the message that I was on the board of. I'm thinking in my head, I'm like, if you're saying this to me, I can't imagine what you're saying to other women. But one of the self-appointed people that have the self-appointed angry uncle in the Middle East, bring Masjid as one. By the way, all the churches have him, all the synagogues have like, I was very like, I was so relieved to find out we weren't the only ones that have this person. But the designated angry uncle at Masjid, he comes to me, he's like, let's be clear, I don't want to see you here again. I pointed to the spot, I'm like, here uncle, Allahu Akbar. I prayed, in that spot for two weeks straight. He come in, I point to the spot, Allahu Akbar. I didn't raise my voice. I didn't raise my voice, I didn't argue with it, like, I knew it wasn't going to work. But I was not going to give up that space. I'm not going to give up the space that Sayyidina Maryam, alaihi salam, created for us. I was never going to give up that spot. SubhanAllah, afterwards you would see me turn around. Alhamdulillah, I don't... SubhanAllah. I just, I think it's really important for us to know our own tradition. And to not accept what junk people have told us. I was preparing a talk, we have an interfaith group and I was preparing a talk and I was like, it would be really great if I talked about Rabia al-Adouya, alaihi salam. And everything that I looked up in English was, there is no way women in an Arabian society had power like this. But Rabia had everyone and all the leaders like listening to her. And I'm like, aren't you disproving the point you're actually making? It's so... How are you saying, in one sentence all like Sayyidina Maryam, alaihi salam, alaihi salam, alaihi salam, I guess he's one of the taberns. She decided in one of the sessions that he was sitting with her that he talked too much about the dunya and banned him from coming back. He's one of the greatest scholars of her time. And she's like, I don't like this guy, he doesn't come back. He's never right to my time. They went and asked her for advice. This is not new. We have always been doing this and we handed off one generation after another, whether we know their names or not. The story of Sayyidina Musa alaihi salam actually begins with his mother talks about his sister. We don't know their names and we don't need to know their names because mothers do this. Sisters do this. The men needed to be stated by name because what they were doing was exceptional among the men. Honestly, Alhamdulillah, we have so much dignity from Allah SWT. May Allah allow all of us to live out what Allah has written for us. May we meet the Prophet Sayyidina Musa alaihi salam and all of these women that we talked about, maybe be proud of us. Maybe live our lives in a way that makes them proud of us. I mean, Jusahb al-Naghair and Allah SAW, praise and blessings be on his beloved Prophet Sayyidina Musa alaihi salam. May Allah have mercy on him. May Allah have mercy on him.


New record from Ukrainian White Wolf 20 Russian targets destroyed Fighters of the special group Alpha of the security service of Ukraine White Wolf Destroyed 20 enemy targets in one night. The special forces published a video with fragments of their combat work The achievements of Ukrainian soldiers include eight tanks three MSTAS self-propelled artillery systems three D-30 howitzers one armored combat vehicle and five Fortifications with at least 17 Russian occupants our special forces men created a real hell for the Russian occupiers And they dispelled the darkness with the fire of burnt enemy equipment the commentary to the video reads Special group Alpha is an elite Ukrainian Spetsnaz group branch of the security service of Ukraine and a successor of the Soviet Union's Alpha group Group Alpha is one of the top divisions of the special forces of Ukraine in recent months armed forces of Ukraine have become one of the most Consolidated armies in the world today Ukrainian reconnaissance deals with special operations behind enemy lines military reconnaissance determines the effectiveness and weaknesses of the enemy during combat and provides its own forces with information for planning tactics in battle It is the reconnaissance who detects the position of the enemy's artillery tanks and anti aircraft installations


You know who else fell to right now in the draft moist critical is here. Charlie. Oh my goodness. What is up, man? Charlie is a Tampa Bay guy actually. Oh, really? Yes, Charlie is a Tampa Bay guy. He did he did a video with the Gronkowskis Oh, I did not know that. Yeah, he did. So Charlie, how do you feel about that pick brother? I'm gonna be honest I don't know who that is but he's that one was looking a lot like I would love to go to a Bucks game someday I think I think going to your game and Raymond James would be Will be phenomenal Raymond James goes hard every touchdown they're fire off the cannons. It's really hype really really appreciate you coming out and And talking to us today. Hey, thanks for having me out and Godspeed to the Buccaneers We lost Tom Brady, but I still believe in the squad. We also lost all our fans with him, but


Now, there is the couple of points I want to make and then I will state one proposition. So, so consider, did somebody have a question, was there a question? So I'm defining an orthonormal square matrix, yeah go ahead, okay, so let's consider an orthonormal square matrix. This is a matrix such that it has orthogonal and unit norm columns, that's the definition of an orthonormal matrix and it has the property that another way to define it is a matrix Q satisfies Q transpose Q equals Q Q transpose equals the identity matrix. So by the way, in general, it's always true that for square matrices, if AB equals the identity matrix, then BA is also equal to the identity matrix, okay, this is easy to see. If BA is not equal to the identity matrix, then BA minus I is non-zero, which implies now if I pre-multiply by A, then ABA minus A is not equal to zero, but AB is equal to the identity matrix, so which implies A minus A is not equal to zero, which is a contradiction, okay. So for square matrices, it's always true that if AB equals I, then BA equals I, therefore, if I say Q transpose Q equals I, then Q Q transpose must also be equal to the identity matrix. So, there is another definition for an orthonormal matrix, which is the definition I'm going to use for stating this proposition, which is that a matrix A has to be equal, yeah? Sir, in above proof, BA, we are taking not is equal to I, yeah, so why I am writing ABA is equal to A? AB is equal to I, right? If AB equals I, that's what we are trying to show here, that if AB is I, then BA is not is must also be equal to I, so AB is equal to the identity matrix, identity times A is always equal to A, whatever A is, yes sir, thank you, yeah, I have a doubt, so on the top you have written Q transpose Q equals Q Q transpose equal to identity matrix, but the dimension of Q transpose Q will not be equal to the dimension of Q Q transpose, right? Square. Oh, okay, it's for n cross n, okay fine, okay, if it is, suppose if it's in rectangular matrix, then how will this? Then it's no longer true that if Q transpose Q is I, then Q Q transpose must be equal to I, okay, but either of them will hold true, right, like at least, I mean, if one doesn't hold true, then other will definitely hold true, right, in case it's an orthogonal matrix. So if the columns are orthonormal, then Q transpose Q will contain as its entries inner products between columns, okay, and so that will be equal to the identity matrix, but Q Q transpose need not be the identity matrix, okay, similarly, if the rows are orthonormal, then Q Q transpose will be the identity matrix, but Q transpose Q need not be the identity matrix, okay, fine, okay, sir, yeah. So this is said to be an orthonormal matrix if it preserves the inner product. So what I mean by that is, if I take the inner product between ax and ay, that is equal to the inner product between x and y, for every x and y belonging to r to the n, okay, so that's also another definition of an orthonormal matrix, okay. So here is the proposition, so the following statements are equivalent, A is, so here A is a matrix in r to the n cross n, B is, A preserves the length, by that I mean, A v for every v in r to the n, so recall, okay, that's the definition of the, in fact, for the moment I won't write the subscript 2, because this result is actually more general, it doesn't require the inner product to be defined the way we have been defining it until now, we've seen only one example of an inner product, there are other possible definitions for the inner product, but right now we are working with the dot product as the notion of the inner product, but any other valid notion of the inner product can be used to define a norm defined like this, okay, and that is called a norm that is induced by an inner product, and this is true for any definition, any valid definition of an inner product, okay. Can you explain the previous definition, A x, A y equal to x, y, what is A x, this is a column? Yeah, x is a vector, so A x is a vector, so it's looking at the inner product between A x and A y. Okay, so what is x and y, it is numbers or vectors? It's right here, x, y belongs to r to the n, so if it's a column 1 and column 2, it will be 1 and 2. What do you mean, x is a vector in r to the n, y is a vector in r to the n, x and y are vectors, x is a vector and y is a vector, so if you compute the inner product between x and y, whatever number you get, this is the same number as what you would get if you computed the inner product between A x and A y, and that's true for any pair of vectors I choose. Okay, I think this is important that everybody understands the definition, otherwise this entire proposition makes no sense. So do you have other questions about the definition of an orthonormal matrix? Please ask, the definition is that it should preserve the inner product, that is you take two vectors in r to the n, if you find the inner product, that is x, y, and then you take A x and A y, those are also two vectors in r to the n, and you find there inner product, and those two numbers must be equal for all pairs of vectors in r to the n, not for just one particular pair. Sir, actually in the inner product line, a matrix into a vector is actually a transformation, right? Yes. So what is the meaning, I mean, inner product is actually the length, I mean, the component of x along y or something in that sense, right? I mean, inner product between x and y means the component of x along y. Correct. So it's preserving the relative orientations of x and y, that is what it means. Okay. In whatever frame we transform this vector. Yes. Yes. So if, for example, x and y were orthogonal, they were perpendicular to each other, but collinear with each other, then even after transformation by A, they will remain collinear with each other. That's what it means. Okay. Okay. And mathematically, this is the precise meaning of a matrix being an orthonormal matrix. It preserves all inner products, not just when x and y are orthogonal, or not just when they are collinear. Thank you, sir. Hello, sir. Just a question, like it is, when a multiplied a vector with A, it's not changing the length. So is it, it will rotate the vector? Yeah. That's a good way to think about it. It will rotate the vector, but it will not change its length. So in some say, so another way to put it is that every rotation matrix is actually an orthonormal matrix. And every orthonormal matrix can be thought of as a rotation matrix. Okay, sir. Sir, is this sometimes called orthogonal matrix as well? Yeah. So that's actually some, that's actually a good point. Depending on the textbook, some textbooks refer to this, this kind of matrix as an orthogonal matrix. Some textbooks refer to it as an orthonormal matrix. I prefer the terminology of orthonormal matrix because it also clearly tells you that every column is unit norm. An orthogonal matrix, if you really wanted a more general definition, it is a matrix where the columns need not be unit norm, but they are still orthogonal to each other. Okay, that could be a more general definition of an orthogonal matrix. But yeah, just to be clear, I want to call it an orthonormal matrix in this course and it's a matrix whose columns are unit norm and are orthogonal to each other. These are two equivalent definitions, but for the purposes of showing this proposition, I will go with this definition, meaning that it's an orthonormal matrix if it preserves in a product. So the third property is that A transpose is equal to A inverse, A is an invertible matrix, which means that A transpose A equals A transpose which equals the identity matrix. And the fourth property is that the rows of A form an orthonormal basis for r to the n. And the last one is that the columns also form an orthonormal basis for r to the n. Okay, so how do you prove such a proposition? So it says that these statements are equivalent, meaning that if I tell you that A is orthonormal, it's the same as me telling you that A preserves length. So if you have five statements like this, the way to show that all of these are equivalent is to say, for example, you take the first two statements, you should show that A implies B and B implies A. That means A and B are equivalent. Then you take the third statement C, then what you have to show is that either A or B, one of those two statements implies C and C implies either A or B, one of those two statements. Then it means that A, B and C are equivalent. Then similarly you take D and you show that D implies one of these three statements, A, B or C. And you should show also that A, B or C, one of these three statements implies D and so on. If you show all of that, then you've shown that these statements are all equivalent. Of course, there are many ways to do it. For example, you show A implies B and B implies A, then you show B implies C and C implies B, then you show C implies D and D implies C and D implies E and E implies D. So that also means that these statements are all equivalent. So let's see how to show this. So first we'll tackle A implies B. So we want to show that if A is an orthonormal matrix, then it preserves the length, meaning that for any vector, if I look at the length of V, it's equal to the length of the transformed version of V, which is A V. So and vice versa. If A preserves the length of every vector in R to the N, then A must be an orthonormal matrix. So to show first A implies B, an orthonormal matrix implies that it preserves the length, then what I need to do is I just need to consider the inner product between AX and AX. And this, the inner product between AX and AX, because A is an orthonormal matrix, by definition it preserves inner product. So basically this is equal to the inner product between X and X. So that means that if I... So this is nothing but AX squared and this is nothing but X squared, which means that AX equals X. So this means that... So this is what we wanted to show that A preserves length. So A implies B. Similarly, B implies A. What I need to do is I need to show that if A preserves the length, then A is an orthonormal matrix. That means that all inner products are unchanged by multiplication by A. So what I'll do is I'll consider... Sir, could you explain how inner product of AX with itself is equals to inner product of X with itself? That's from the definition. So what I want to show here is that if A is orthonormal, then it preserves length. So if A is orthonormal by definition, because it's an orthonormal matrix, it preserves the inner product. The inner product between any two vectors. In fact, Y need not be equal to X. So if A is an orthonormal matrix, then AX, AY is equal to the inner product between X and Y. This is true for all pairs of vectors X and Y. And so all I'm doing is to take a special case of this, where Y equals X. So the inner product between AX and AX is equal to the inner product between X and X. So you can see that although the statements look quite different from each other, saying that A is an orthonormal matrix, meaning that it preserves inner products and saying that A preserves length, they seem different from each other in terms of statements, but in fact, it follows trivially from the definition. Is it clear? Yes, sir. Thank you, sir. So if I take the inner product between AX plus Y and AX plus Y, this because A preserves length. So now I want to show that B implies A. So A preserves length. So this is nothing but the length of A times X plus Y square. And so this must be equal to the length of X plus Y square. But if I expand this out, by using the linearity of inner products, then this thing can be written like this. It's the inner product between AX and AX plus two times the inner product between AX and AY plus the inner product between AY and AY. And the right-hand side, if I expand this out, I get the inner product of X with itself plus two times the inner product between X and Y plus the inner product between Y and Y. Now once again I use the property that A preserves length. So this quantity inner product between AX and AX, this is equal to the inner product between X and X. And this term is equal to the inner product between Y and Y. So this XX will cancel with this XX. This YY cancels with this YY. And the two and two can cancel. So you are left with AX, AY equals XY. So it preserves inner products and so then it is orthonormal. Then we consider C, the statement C. So the moment you are considering inner product of AX, AX is X, X. So that moment only you are considering it to be orthogonal, right? That is what they are showing here actually. Yeah, but in the second last step you already considered AX, AX is X, X. So what we are trying to show here, I think it's important to pay attention a little bit to what we want to show. So what we want to show is that B implies A. What is that? If A preserves the length, that is if norm of AV equals norm of V for every V in R to the N, then A preserves the inner product. That is the inner product between AX and AY is equal to the inner product between X and Y for all XY in R to the N. That is what we want to show. And that's what we are doing here. It's not a difficult proof. It's very simple. But it's good to keep in mind exactly what it is that we are showing. So in writing the first step, I'm using the fact that B is true. I'm saying if B is true, then I want to show that A will preserve an inner product between any pair of vectors. So this is true because A preserves the length. This is also true because A preserves the length, AX, AX equals X, X. That's also true because A preserves the length. And similarly, AY, AY equals YY is because A preserves the length. And a consequence of this is that I'm getting AX, AY inner product is equal to the inner product between X and Y, which means that A is orthonormal. Sir. Yeah. Sir, so you gave the definition that an orthonormal, it's an A is an orthonormal matrix if it preserves the inner product. But that statement does not speak about the converse. That is, if it preserves the inner product, then it should be orthonormal. That part is not implied by the definition, right? Yeah. So this is also a very good point. In mathematics, a definition is always an if and only if statement. Okay. So we write it like this. A matrix is said to be an orthonormal matrix if it preserves the inner product. But when we are saying that it is said to be or it is defined as an orthonormal matrix, we mean that this is an if and only if condition. Okay. Okay. Okay. By definition, an orthonormal matrix is one which preserves the inner product. All definitions in mathematics are like this. We define something to be in a particular way. It means that A is equivalent to B. If I define A to be equal to B or A to B, or if I say a matrix A is defined to have a property X, if it satisfies Y, it means that X and Y are equivalent to each other. Okay. Now, let's do the next step. Next. If I consider the inner product between AX and Y, I will make a statement. This is equal to the inner product between X and A transpose Y. This can be seen by just writing out the expansion of what this will be. So, basically, this AXY is nothing but summation i equals 1 to n, sigma j equals 1 to n, Aij, Xi and Yj. And if you expand this out in terms of the entries of A, you will find that this is also exactly the summation. So, I should say. Okay. So, now what I can do is instead of Y, I will replace Y with AY. Then what happens is that I get, so I should write that out so we don't have confusion later. Then what I get is the inner product between AX and AY. Now, because, so suppose A is an orthonormal matrix, then it preserves inner products. So, that means that this is equal to XY. And this is equal to the inner product between X and A transpose A times Y. And this is true for every X, Y. So, if A is orthonormal, then we have that this is equal to this for every XY in R to the N. So, then that means that what I can do is I can take example vectors for X and Y, X equal to EI, the ith column of the identity matrix and Y equal to EJ, where EI equals the ith column of I N cross N. Then what I have is, if I consider the left hand side, this EI EJ. So, EI EJ is equal to, I can write it as delta IJ, which is this equal to 1 if I equals J and 0 otherwise. Then the right hand side is the inner product between EI and A transpose A EJ, which basically if you expand this out, you see that you will see that this exactly pulls out the IJ ith entry of A transpose A. So, that means that the IJ ith entry of A transpose A is delta IJ, which means that A transpose A is the identity matrix. So, then it means that A is A transpose is the inverse of A, A implies C. So, we have that. Now, conversely, if A transpose A is equal to the identity matrix, then if I consider the inner product between X and A transpose AY, this is equal to, this is the identity matrix. So, this is always equal to X and Y, the inner product, because A transpose A does not change Y at all. But then the left hand side, this, I can move this A transpose over here and I can, so more generally, so let me just write it like this, X A transpose times AY. I will consider this to be some vector, A transpose times something is equal to the inner product between AX and AY. And so, thus, AX AY equals XY for all XY in R to the N and does C implies A. And the last step is just that, if A transpose equals I, it means that the rows of A are orthonormal. So, we have seen that, so these two are equivalent statements, because this is just computing the inner product between rows of A. And if this is equal to I, it means if I take any pair of, any distinct pair of rows, they are orthogonal to each other. And if I take any row, it has unit inner product with itself. So, the rows of A are orthonormal, they are both equivalent statements. And so, C implies D and D implies C. And similarly, A transpose A equals I is the same as saying that the columns of A are orthonormal. Yes. Sir, in order to show that inner product of AX and Y is same as inner product of X and A transpose Y, can we use this formulation that inner product of X comma Y is same as A transpose Y? Yeah, it's the same point. Yeah, it's exactly the same point. Yeah, it's exactly the same point. This is it. This is the point. Because, you know, this summation sometimes does not click how to write in form of this or two summations. But directly doing the transpose, we can easily separate it out. Yeah. So, but that will be valid. Yeah. So, you can do it that way also. Okay. Okay. Thank you. So, the thing is that, you know, it follows from the definition of the inner product that we said. So, you have to take the transpose of the first vector and then multiply it with the second vector. So, if you think of it that way, it follows immediately. That's also a valid way to write it out. Okay. Any other questions? Sir, is that true for all A? No, right. Of course, this is always true. AX comma Y inner product is always equal to X comma A transpose Y. What the previous student just said is that if I think of X, Y to be equal to Y transpose X, if I think of it this way, which is how I defined the usual inner product earlier, then if I were to take AX and Y, this is equal to Y transpose AX, which is also equal to A transpose Y whole transpose times X. Yeah. And which I can write as X transpose times A transpose Y. No, I don't need to do that. To prove the equivalence of five statements, we are actually going through ten proofs, but actually six proofs would suffice, right? Because A implies B, B implies C, C implies D, D implies E, then E implies A, then all of them will imply each other. Yeah. So, that's also a valid way to show it. There are many ways to write out this proof. I've shown you one way here.


gonna learn about some big money or unexpected bolos. Hey, Bolo buddies, thanks for watching. Amazing, right? All right, let's get started. Hey, Bolo buddies, thanks for watching. It is time for This Is My Bolo. This is where I reach out to my featured members and I'm like, send me a video clip of your best Bolo. Tell me where you got it, what you paid for it, and what it sold for.   Thanks so much for being here and be sure to subscribe and let's get started. Chen, all right, you guys, this is my Bolo. I got these at a garage sale for one dollar. They are vintage chenille pipe cleaners. I'm gonna pop it up right here so you guys can see it better. One dollar I paid for them at a garage sale and I sold these for 77 dollars and 50 cents. The buyer was all in for 93.11. You guys, these are arts and crafts, but they're vintage and they are collectible and people use them and need them and they're hard to find. So definitely be on the lookout. This is a nice little bundle, but 77 dollars plus tax and shipping. Woohoo! This is my Bolo. Hey guys, my name is Tanya and I'm just a girl out here making a living thrifting and my Bolo is this. This is actually some fabric. I saw Courtney's post on the community page to get our videos in and this was actually already packed up to go out today. So I'm going to put the screenshot up here for you. This, I actually purchased this fabric from a thrift store when my husband and I went to Flipcon and I noticed that some of the Holly Hobby fabric went super high and some of it went super low on eBay. So I decided to do an auction, which is not normal for me, but that's what I do when I can't decide how to price it. I believe I started the auction at $79.97 and within a few hours I received one bid on it, ran it for seven days, didn't receive any more bids on it and the buyer actually sold after the seven day auction. I didn't even have to send him a reminder. Can you believe that? Hey Bolo buddies, how are you? This is Zandra, also known as Piece of Scrap. I'm a reseller on eBay, Facebook, Poshmark, McCarrion, Amazon and here is my Bolo. I picked up this Hallmark Jingle Pows Snowman and Dog Animated Battery Operated Figure at the Benz for just about $2.00. I paid $1.79 at the Benz and this weighed a little over one pound. I wasn't sure if it worked or not, so I took it home and put batteries in it and guess what? It works. I included that video in my eBay item description and it sold on my promotion for $66.83 and the buyer paid $12 shipping, so they were $78 all in. Follow me over on YouTube at Piece of Scrap for many more what sold on eBay, Poshmark, Facebook and McCarrion videos. Thank you Courtney. Hi Courtney, this is Cher, grinning grandma and my Bolo this time is a set of 10 caviar dishes. They were actually made of mother of pearl and shaped like fish. We got them at an estate clean out, which basically means that we didn't have any cash into it at all, just our labor for the clean out and they sold for $155. The buyer did pay for shipping. Yay. Hello, this is Eric, better known as Ohio Treasure Hunters and this is a Bolo I'm showing.  It's Pokemon, it's video games, you know, they both sell. However, in this case this has no game in it. It is just the box and a really beat up manual. That is all. Okay, I got this at the Goodwill Benz. I paid pennies for it because it weighs like nothing. I had it listed for $149.99. I took a best offer of $110 plus shipping for it, but this is just a reminder. Don't just keep an eye out for video games. Don't pass up on high value video games on boxes and manuals because they hold value as well. Love your sales and dreams over on eBay, Instagram and YouTube. Go check them all out. You guys subscribe, follow whatever you gotta do. This is my Bolo. So I'm in the car right now obviously but I'm going to give it to you. I paid $20 for these industrial style lights. The name brand on these are Abolite, but the name doesn't really mean so much. The fact that they are industrial and that they are very heavy duty galvanized, they're going to last through the weather. If you guys see these at a yard sale or in a state sale, thrift stores, whatever, and they are decently priced, go ahead and pick them up. Ended up selling them at a final price of $400 that I accepted on a buy it now. I initially listed them in my store for $700. I'm the type of person who is going to list something a little higher so that I can put it on sale and I'll still be able to accept an offer and make a very nice profit. You guys, I'm Danielle and that's my Bolo. Howdy Bolo buddies. My name is Gretchen and I am the Restless thrifter and I am a part-time reseller and part-time dog sitter. I want to talk to you about Coors Pottery. You know, Coors like the beer company, did you know that they used to make dinnerware and cookware? During prohibition, they had to shut down the beer line so they had to switch gears and they started making pottery. They made it from the minerals in local mines in Golden Colorado where the company is founded. It's very colorful and collectible and very reminiscent of fiesta ware. But I want to show you the Bolo's that I have sold. It doesn't sell really fast but it is a really cool piece of history so if you see it, look it up. I sold a couple of pieces of the rosebud line. I sold this casserole dish for $55 plus shipping and then this mixing bowl set. It sold for $70 plus shipping. You'll want to look for these stamps but not everything is stamped so in the rosebud line you can look hopefully for those telltale roses. Thanks for watching and if you want to see more Bolo's and more dogs, feel free to follow my channel The Restless Thrifter. I do thrift hauls with average sales price and sell-through rate as well as weekly sales updates giving you my profit. Thanks everybody. Hi, I'm the Rebel Reseller and I'm going to be sharing this is my Bolo but first I wanted to thank Courtney for all that she does for YouTubers and resellers. This circus clown, I picked up at the Nashville Bins when I was out there participating in Courtney's Bins Bingo Challenge. It is by My Lai. I checked eBay. There were no comps. Tara Peak. I went back the two years. There were none and then when I went on worth point there was only two similar clowns that had sold for $40 and $50. I knew that this was something special so I listed it very high at $199.95 and within a couple of days I received an offer of $120 which I accepted. Thank you. Hi friends, this is Toy Attic and this is my Bolo. This My Scene Barbie Masquerade Madness Doll sold in about three days for $135 full asking price. I paid $4.50 for her at an estate sale and I also bought this other one that's sold in about the same amount of time for $115. I guess I shouldn't have taken an offer. I wanted to bring these up as my Bolo because a lot of people think that Barbies are not really worth that much and Barbie is actually very hot right now. So especially Barbies from the 80s and 90s and of course older the older they get the more expensive they are but Barbies from the 80s and 90s can be really hot right now. There's several Barbies from the 90s that are selling for hundreds of dollars on eBay. So if you happen to see a Barbie in a box look it up. Thanks for watching. Thanks for all you do Courtney. Please subscribe to my channel Toy Attic or you can follow me over Instagram at Jody Toy Attic. Bye. Hey everyone my name is Crystal and my YouTube channel is Vintage Booth Pro where I focus mainly on my vintage booth sales but I also have an online eBay store and sometimes remember to share on Poshmark. So this sale is about an item that was not only in my booth, not only on eBay but on Poshmark and it finally sold. Let me show you these tiny little Mary Inglebright bird houses ornaments were wrapped up in a bundle of plastic wrap for $1 at Goodwill and they just sold on Poshmark for $75. So I'm always on the lookout for Mary Inglebright and I am going to focus on cross posting some more of my items. Consider checking out my channel if you have a vintage booth or are thinking about it as a way to extend your online sales. Thank you Courtney. Hi everyone I'm Kat and my eBay store is Kat Bill and Thrifty and this is my Bolo. Just kidding this is my sidekick Roscoe goes just about everywhere with me. This is my actual Bolo. It is a ceramic mold Kat with glaring green eyes. The name of the mold on the bottom was E-L-E-Y. Not sure how to say it but I knew the minute I saw it had to be a Bolo black cat green eyes and it was. It sold within 24 hours of me listing it for $45 plus shipping. I picked it up at an estate sale clean out for $10. Not bad. Courtney thank you for allowing me to do this and thank you for promoting all of us in our businesses. I hope everyone has a safe and happy new year and of course a prosperous 2023. Thank you. Hey guys so I'm doing this is my Bolo. My name is Sarah. I also go by Sam because those are my initials. Anyway I wanted to share with you this because I found them at the bins. Would you all believe that at the bins? So I dug and dug because I'm a digger because I know things sink to the bottom. So I dug and I came across these foes headphones and I was like oh my gosh they had a case they had all the accessories needed and I ended up auctioning them off on eBay for $191. So I will take a dollar and put it on eBay and make $191 every day of the week. Anyway I was so excited. This is my Bolo and thanks for watching. Hi my name is Terry. I go by the name Mindful Recycle on my YouTube channel and in my eBay store. My Bolo today is a roasting pan. It is Magna Light and I have sold three of these in the past month and a half to two months. So I paid $20 for this one and I sold it for $149. This other one here I paid $50 for and it sold for $225 and the last one who is not in that greatest shape I paid five bucks for it and it sold for $40. They are super easy to ship because they're indestructible. So look out for these because they do sell really well. Thank you Courtney. Hey Bolo buddies and friends this is Faith with MacPack Co eBay store. We wanted to share our December Bola with you which was a 1993 vintage Avon My First Nativity set. We bought it at a local thrift store for $3 and three weeks later we sold it on auction for $120. The buyer was all in for $141 including shipping. Happy sourcing. Hello everybody welcome back to the reseller cottage. It's Donna. Donna tell about Tolino. Thank you so much Courtney for putting together these videos. You are amazing. I can't believe how awesome you are always promoting other channels and thank you for that but I don't list very often on eBay. I am trying to vamp up my eBay store just a little bit so that I'm not putting all my apples in one basket and by that I mean I sell just strictly on YouTube. I don't sell on whatnot and I very rarely sell on eBay. I used to have 4,000 listings on eBay but now I cater to the reseller but I did find one of this little charm. It's Winnie the Pooh and Piglet. It's a Disney little charm and it was going in one of my mystery reseller boxes which I sell often to my viewers. So if you get a mystery box from me make sure that you look everything up because who would think $40. I'm going to put the listing right there. I just sold it today. So this is my Bolo and again Courtney thank you so much for supporting me and supporting my channel and supporting so many of us and we will see you live. Bye. Hi Courtney. It's Yvonne. Mom knows precious and I wanted to share my Bolo. I sold this today for $90 plus 4.25 shipping and I purchased this on an auction. Records do well. Do your comps. I purchased this on a YouTube auction. I purchased this and one other record that I sold for $41. This one sold for 90 plus shipping. For the bulls I paid $25 so this was $12.50 and I turned that into $90 plus shipping. So look out for records but as you can tell this record is in beautiful condition and near mint condition. I add brand new sleeves. I use the correct packaging. Records can do well but do your research, do your comps and you might score yourself a Bolo. Hi everyone. Tea auctions for you. Thanks for joining. Here is my Bolo. So we had sold this Star Wars attack of the clones carded figure new old stock. Pick this up. I think it in the state sale. I don't honestly remember. I paid, there was a bunch of them. I paid $2 each for these. We sold these for full price at $99.99 with $8.95 in shipping. So that was a great pickup for us. Courtney as always, thank you for doing this and guys thanks for watching. Hi Bolo buddies. I'm Wendy with Nina's Jewels. Here with my Bolo which is James Bama artwork. James Bama was born in 1926 and recently passed away in April of 2022. He's an American artist known for realistic paintings and etchings of western subjects such as Native Americans, cowboys and rodeos. I would describe his artwork as extreme realism. In fact when you look at a James Bama piece you're probably going to immediately think it's a photograph. It is so realistic looking. Even if his artwork is not something that is your style you cannot help but be impressed by his talent. We are very lucky because we have acquired a lot of James Bama prints through another business that we own which is a custom picture frame shop. But if I ever saw a James Bama print out in the wild I would snatch it up so fast it would be like here are three recent James Bama prints that we sold. The first one was called Mountain Man with Rifle. It sold for $350. The next one was called Kin Blackbird in a Sin Boin Sioux. That one sold for $209.99 and the next one was our highest James Bama sale ever and we actually have another one of these prints with multiple washers. This one was called Winter Trapping and it sold for $799.99. Check out our Nina's Jewels YouTube channel and also check us out on eBay. We're also Nina's Jewels there. Bye. Hi Bolo buddies. This is Carrie from Be Carried Away. I have to do a voiceover today because I am still recovering it. So this is my Bolo. These are some felt green Mary Jane style shoes. My favorite category to sell in are shoes and I have a video of when I found these. I was so excited because they're Gucci.  So I picked these up for $3.99 believe it or not and I sold these for $202 and plus shipping on eBay. So definitely don't overlook shoes, don't overlook vintage shoes and when you see that Gucci mark you know it's just possible that it really could be the real deal on these absolutely were. So super excited to pick up Gucci. Okay let's try this one more time. Hey guys Noel Farm Girl Scavenger here and I have a Bolo for you. I have been picking up jewelry for quite some time and I have gotten to the point where I know a little bit. I know enough to get myself in trouble right. So I was at an estate sale today is Monday a week ago and she had some jewelry and I kind of looked through it and then she picked up a little box and she said I have this set here that I have $100 on and I just kind of looked in the box and I looked at it and I said I'll pay $100 for that and she goes you will and I go yeah. I had no clue what it was. I could just tell that it was worth something. And don't ask me why, don't ask me how. Anyway it is a vintage from the 1960s Hobay H-O-B-E with a little thing over the top of it, peaking glass, an Australian crystal, necklace, brooch and earrings set. Now a lot of these sets came in four. There would have been a bracelet with it. Some of these go for over a thousand dollars. Some of them just for the brooches, the necklaces. I probably could have gotten more for it had I asked more for it. But I listed it for $699.99 knowing it would go into my 30% off sale which it did. Somebody bought it outright. I took best offer off because I was offering 30% off and so I ended up selling this for $489 and with $8.75 shipping so all in let's see what did they pay all in. It's actually going to Japan. It's going to a freight forwarder. It's just going across the river to Portland as a matter of fact. They are $498.74 all in with shipping impacts. Something to note this is I will put a picture up too. I don't know how well I'm going to be able to show you how beautiful this is. Maybe I can put a little more light over here. I don't know. One thing I want you to know about Hobay or Hobie, see where it's marked right there? Very few of the earrings. Isn't that gorgeous? Very few of the earrings and the necklaces are marked as what I've seen. Here is the necklace. Look at that bling. And I saw somebody had the brooch. So look them up. H-O-B-E. You will be amazed. And if you're going to start picking up jewelry or if you already know about it, just know that sometimes you need to use Google and sometimes you need to know just because something is not marked doesn't mean it's not worth something. Okay. Have a great day. And Courtney, thanks so much for all you do. Everybody, make sure you subscribe to this girl. She is a working, working, working crazy lady and she does amazing stuff for you. Thanks a lot. Bye. Hey, it's Rhonda with Got Junk in Our Trunk and this is your bow love for today. My daughter Samantha and I went on a girls trip to Mountain View, Arkansas in early fall. And as we were going through, we were stopping at some of the thrift stores on the way. Little country ones, mom and pop type of things. Once we got to Mountain View, we actually found two yard sales on that Saturday. So one of them that we went to was a rural one. And she had a little pile of these type of items and I asked her what she wanted and she said free. Well, there's nothing like a free Oscar Meyer wiener whistle. You will see these when the mobile comes through the Oscar Meyer mobile, I think is what they call it. It comes through and they do demos and different things like that and tell about the history of Oscar Meyer company. And they give these little whistles out you blow in the end here. And of course, it's a whistle. It's actually a whistle. Kids used to love to get things like this. There are all different ones. This one's one that's on top of what it looks like a skateboard. But this is actually what the wiener whistle looks or the wiener mobile looks like a whistle or the whistle looks like it. They look like each other. I got eight of these free. Now, I have to look at my notes to remember how I sold these. I listed the first one for 1199. I always had shipping on everything. I listed these on ebag cross listed it to a couple of different platforms, including Etsy, because these were actually vintage ones. She housed the wiener mobile in her yard and she had some of these left over. And this was from like 25, 30 years ago or something like that. She said, I don't know, but I do know that these are vintage. I saw the first one for 1199. I saw the second one and the third one for 1199. And I decided to raise the price. I raised it to 1599 and ended up selling two of those. All of these at that time had sold on Etsy. So I pulled them off of eBay. Nobody was doing anything over there and I decided to just leave them on Etsy because I knew that I could get a little bit more for them on Etsy because it was a vintage platform. I raised it to 1899, sold one. I raised it to 1999 and sold one. This is the last one that's going out. I sold it for 2999 plus shipping. That's your Bolo for today. Look for the wiener whistle. All right, Bolo buddies. How about those Bolo's? They were fantastic, right? Go down to the description and click on these eBay stores and heart them. That will allow you to follow them. You will get updates when these eBay stores post coupons and new items. Also, be sure to subscribe to all of these YouTube channels. They are fantastic reselling channels. So that means they have reseller content. And two of the channels sell to us resellers. And that is Donatello Badalino and Auctions for you. They're linked down below also. So if you're looking for inventory, definitely check them out. And I am also selling on whatnot. So if you guys want to come check out my whatnot auctions, I will link that down below as well. Thanks for watching. Also update, got the Bolo buddies hat merch. It's linked down below. If you're interested, turned out great. Also, if you're new to the channel, let me know how you found Bolo buddies. Thanks for watching.