Complementary triangular forms of pairs of matrices, realizations with prescribed main matrices, and complete factorization of rational matrix functions
By definition, \(m\times m\) matrices A and Z admit simultaneous reduction to complementary triangular forms if there exists an invertible \(m\times m\) matrix S such that \(S^{-1}AS\) is an upper triangular matrix and \(S^{-1}ZS\) is a lower triangular matrix. Several sufficient conditions for such an S to exist are given. There is a connection with the problem of complete factorization of a transfer function.
scientific article; zbMATH DE number 4051807