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Linear AlgebraHardSingular Values & the SVD

Singular Values & the SVD · Hard problem

A 5×55\times 5 data matrix AA has singular values 12,8,4,3,112, 8, 4, 3, 1. What is the smallest kk for which the truncated SVD AkA_k has relative error ∥A−Ak∥F∥A∥F≤0.1\dfrac{\|A - A_k\|_F}{\|A\|_F} \le 0.1?