Lecture 29: Singular value decomposition

For more general A, the SVD requires two different matrices U and V. We’ve also learned how to write A = SΛS−1, where S is the matrix of n distinct eigenvectors of A. However, S may not be orthogonal; the matrices U and V in the SVD will be. How it works We can think of A as a linear transformation taking a vector v1 in its row space

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