On the Simultaneous Reduction of a Pair of Unitoid Matrices to Diagonal Form

Let A and B  be Hermitian n*n  matrices with A  being nonsingular. According to a well-known theorem of matrix analysis, these matrices can be brought to diagonal form by one and the same Hermitian congruence transformation if and only if the matrix C = A-1B  has a real spectrum and can be diagonalized by a similarity. An extension of this assertion to the case where two unitoid matrices are simultaneously reduced to diagonal form is stated and proved.