Simultaneous Diagonalization of Positive Semi-definite Matrices

Abstract

We give necessary and sufficient conditions for solvability of A(j)=XW(j)t(X), with the A(j) are m given positive semi-definite matrices of order n. The solution X is n x p and the m solutions W(j) are required to be diagonal, positive semi-definite, and adding up to the identity. We do not require that p ≤ n.