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[Repost] Help: Inverse of matrix sum
Posted:
Feb 28, 1997 5:47 PM


Hello everyone,
There were no responses to my previous posting, so here it is again.
I need help on the following problem. I have a matrix R: K R = [sum C_i P (C_i)^H] + a I i=1
where ( )^H denotes a Hermitian transpose and 'C_i' is 'C subscript i'. All matrices are NxN. 'C_i' (i = 1,...,K) are diagonal unitary matrices (C_i (C_i)^H = I). 'P' is, in general, a rank N matrix. 'I' is the identity matrix and 'a' is a positive scalar. I am seeking an expression for the inverse of 'R' in terms of 'C_i' or at least the vectors 'c_i' (where c_i = diag(C_i)) and perhaps the eigenvalue decomposition of 'P' (or the SVD of 'P' or some transformation of 'P').
I would greatly appreciate any help in this regard. Even references will do.
Thanks in advance,  Nitin Mangalvedhe Mobile and Portable Radio Research Group Bradley Department of Electrical Engineering, Virginia Tech http://www.ee.vt.edu/nitin/home.html



