Question: (a) Let be an N N diagonal matrix. What is the diagonal matrix that has rank at most r which is closest to ? That

(a) Let be an N N diagonal matrix. What is the diagonal matrix that has rank at most r which is closest to ? That is, solve min 2F subject to is diagonal, rank() r. RN N (b) Show that the Frobenius norm is invariant under rotations. That is, if X RMN is an arbitrary matrix and W RMM and Z RNN are orthonormal matrices (WTW = WWT= IandsimilarlyforZ),then XF = WXF = XZF = WXZF. Hint: A2F = |aij|2 = TrAAH

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