CSE 521 : Design and Analysis of Algorithms I Spring 2016 Lecture 9 : SVD , Low Rank Approximation

ui = Mvi ‖Mvi‖ = Mvi √ λi = Mvi σi Note that singular values σi are equal to √ λi; since M M is PSD, λi ≥ 0 and σi is well defined. In particular, observe that if M is a symmetric matrix, σi is the absolute value of the i-th eigenvalue of M . Now, we want to show that these vis and uis meet SVD conditions. Recall that vi’s are orthonormal because they are… CONTINUE READING