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Topic: [Repost] Help: Inverse of matrix sum
Replies: 0

 Nitin Mangalvedhe Posts: 10 Registered: 12/7/04
[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 eigen-value
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.