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Math · Advanced Math
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3. Let A ERnxm, n> m and rank(A) m. The singular value decomposition (SVD) of A is A-UEVT, where U E Rnyn and V E R,Y, are urilugunal, and Σ E Rnmn has singular (a) Determine the SVD decompositions of the matrices (ATA), (ATA)TAT, A(ATA)-1, and A(ATA)-AT in terms of the SVD of A. Please specify the dimensions and elements of the obtained Σ matrices (b) Use the results of part (a) to determine the matrix 2-norms IKATA)illa, IKATA)냈lla, llA(ATA)-1112, and ll-A(ATA)-1Alla (c) For any matrix A-(aij), A ERnxm, define 1/2 n m This is the Frobenius matrix norm. Show that where ai are the singular values of A.
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