If a vector has zero magnitude, is it meaningful to call it a vector?
Zero vector has no magnitude and direction. Why is it even a vector? What does it mean to be a vector without having magnitude and direction?
Can the vector have a zero magnitude if one of the component is not zero? Why is it impossible for a vector to have a negative magnitude? How do you prove that every vector space contains a zero vector? Can you find a vector that has a magnitude of zero but components that are non-zero? Can anyone clear up my confusion as to how the zero vector is in Nul(A)? Aren't the vectors in Nul(A) the non-zero vectors that make some matrix A equal to 0? What is a vector quantity? What is a vector? WHAT is really a vector? Why are they zeros? I've seen vectors described as direction and magnitude, and also as a one dimensional matrix. Are these concepts somehow related, or merely homonyms? What is the physical significance of vector operator? What is 0 dimension? What is the physical significance of vector space? If Imaginary numbers were made to deal with negative roots, why hasn't a similar convention been made for the division of zero? Can the components of a vector also be a vectors? How is displacement considered as a vector quantity? Can eigen values and eigen vectors be zero? What does zero of potential energy mean? What is the importance of zero? What are the components of a vector? Why do we need the data to have zero mean in neural networks? Why is 0/1 equal to zero? What is the difference between vector and coordinates? Is power a vector quantity? How is this determined? What is a vector in linear algebra? Why do vectors have components and scalars don't? Is it possible that the resultant of two vectors of equal magnitude has same magnitude as the two vectors have? What is the physical significance of dimension of a vector space? Why is anything raised to the power zero is one, but multiplied by zero is zero? What is a vector machine?