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Unformatted text preview: s T /s T s has the smallest 2norm of all m × n matrices E that satisfy ( A + E ) s = y . 7. Let X and Y be two full column rank matrices. We know from problem 5 that there are many matrices A which satisfy the pair of equations AX = Y, Y T A = X T . From the set of all such matrices A , ﬁnd the one that has the least Frobenius norm. 8. Let M be a real symmetric n × n matrix, and let L M be a linear operator from R n × n to R n × n , deﬁned by the equation L M ( A ) = A T M + MA 2 . Deﬁne the matrix (or operator) 2norm of L M (denoted by k L M k 2 ) by k L M k 2 = max k A k F =1 k L M ( A ) k F . Show that k L M k 2 ≤ k M k F . Extra credit: Show that k L M k 2 = k M k 2 . 1...
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This document was uploaded on 01/23/2012.
 Spring '09

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