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.