Theorem18.1The existence of the SVD
Every matrix has an SVD, and the singular values are uniquely determined. If the matrix is square and the singular values distinct, the left and right singular vectors are uniquely determined up to complex sign.
This class when rather slowly, indeed. It was supposed to culminate with a proof of the following.
Every matrix has an SVD, and the singular values are uniquely determined. If the matrix is square and the singular values distinct, the left and right singular vectors are uniquely determined up to complex sign.
However, the timing was very poor, and so we will have to return to this again