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February 1st, 2012, 01:59 AM   #1
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Matrix norm optimization problem

Given matrices C ? R{nk} and X ? R{nk}, it is known that X minimizes the following

?CC^T?XX^T?^2,

which is a summation of squared elements of matrix CC^T-XX^T
Can it be proved that such solution X minimizes

?C?X?^2

Perhaps writing the above as a summation might help.
(The problem is in Linear Algebra subforum, but moderators could link it to optimization problems)
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