

Subject:
maximizing a function of matrices
Category: Science > Math Asked by: elgoog_elgoogga List Price: $80.00 
Posted:
16 Oct 2006 10:19 PDT
Expires: 15 Nov 2006 09:19 PST Question ID: 774065 
Let f = det(X'X)^{m/2} * etr ( Y (X'X)^{1} Y'). Here both X and Y are real matrices. X has full column rank. X' denotes the matrix transpose. X^{1} is the matrix inverse. det(.) denotes the determinant of a matrix. etr(.) is the exponential trace function etr(.) = exp( trace(.) ). m is a constant scalar. Y is a constant matrix. I am interested in finding X that maximizes the function f. 1. If we assume we know nothing about X, and also assume Y has full column rank, then function f has maximum. Dr. Israel has solved this problem. See http://groups.google.com/group/sci.math/msg/742abcca5e9998ec 2. Now the problem is what if we know some columns of X? That is, if some columns of X are known to be fixed, how to find other unknown columns to maximize the function f? Thank you very much.  


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