9g) Diagonalization of Special Matrices (Proof)
Channel: Mark Ancliff
Date: 2015-05-28

In this video I prove the theorem on Special Matrices stated in the previous video. (In fact this video only shows the proof for symmetric matrices, but the other cases (Hermitian, Orthogonal, ...) have similar proofs.)

-- Every matrix has at least one Eigenvector (1:05)
-- An equivalent definition of symmetric matrices (2:40)
-- Proof that an nxn symmetric matrix has n Eigenvectors which can be chosen to be orthogonal (5:20)
-- Proof that the Eigenvalues of a symmetric matrix are real (14:28)