Question: 8. A bit challenging: Prove that the kth singular value of any matrix A is bounded as ok(A)2 0 there exists B with rank (B)

8. A bit challenging: Prove that the kth singular value of any matrix A is bounded as ok(A)2 0 there exists B with rank (B) = k such that ||A - BI|2 5 k+1 . IAE. Here A - B|/2 is the spectral norm, given by A -B|2 = maxx: x 2=1 ||(A -B)x|/2 or equivalently ||A - BI|2 = 01(A -B)

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