For 10 points, name these scalars that, when multiplying a matrix, are equal to the product of a vector with that matrix and which are usually denoted by the Greek letter lambda.
Weyl's theorem can be used to show that the Dirchlet type of these are asymptotic, providing an answer to the Mark Kac-proposed question "can one hear the shape of a drum?"In quantum mechanics, ladder operators alter these quantities by one, and they are taken to be 1 or -1 for the permutation operator. Always real for a Hermitian matrix, they are the roots of the characteristic polynomial, and for diagonal matrices, they are given by the entries of the diagonal. For 10 points, name these scalars that, when multiplying a matrix, are equal to the product of a vector with that matrix and which are usually denoted by the Greek letter lambda.
Weyl's theorem can be used to show that the Dirchlet type of these are asymptotic, providing an answer to the Mark Kac-proposed question "can one hear the shape of a drum?"In quantum mechanics, ladder operators alter these quantities by one, and they are taken to be 1 or -1 for the permutation operator.
eigenvalues [or latent roots; proper values; characteristic roots; characteristic values]