This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005.

/pdf/rotterdam-econometrics-publications-of-the-econometric-z3f13cqk1x.pdf

"Rotterdam econometrics": publications of the econometric institute 1956-2005

Complementary triangular forms of pairs of matrices, realizations with prescribed main matrices, and complete factorization of rational matrix functions

The problem considered is the following. Given two upper triangular Toeplitz matrices A and Z, when does there exist an invertible matrix S such that S -1 AS is upper triangular and S -1 ZS is lower triangular ? The motivation for considering simultaneous reduction to complementary triangular forms of pairs of matrices comes from systems theory. For upper triangular Toeplitz matrices, a complete answer is given. The argument involves a detailed analysis of a certain directed graph associated with A and Z. Along the way information is obtained about the structure of the similarity S. The results actually hold for a class of matrices strictly larger than that consisting of the upper triangular Toeplitz matrices.

Complementary Triangular Forms of Upper Triangular Toeplitz Matrices

The following three problems, are solved. When does a set of companion matrices admit simultaneous reduction to upper (lower) triangular forms? When do two sets of companion matriees admit simultaneous reduction to complementary triangular forms? When does a set of matrices admit simultaneous reduction to companion forms? The results concerning the first two problems involve (combinatorial} conditions on eigenvalues. The question of how to make these results coordinate free leads to the third problem. Its solution is phrased in terms of cyclic vectors. Simultaneous reduction to block companion forms is discussed too. The problem of complementary triangularization is related to that of complete factorization of rational matrix functions from systems theory.

Simultaneous reduction to companion and triangular forms of sets of matrices

https://repub.eur.nl/pub/14334/FactorizationandJobScheduling_1996.pdf

Factorization and Job Scheduling: A Connection via Companion Based Matrix Functions

This paper is concerned with the following questions. Given a square matrix A, when does there exist an invertible lower triangular matrix L such that L-1AL is upper triangular ? And if so, what can be said about the order in which the eigenvalues of A may appear on the diagonal of t-1AL ? The motivation for considering these questions comes from systems theory. In fact they arise in the study of complete factorizations of rational matrix functions. There is also an intimate connection with the problem of complementary triangularization of pairs of matrices discussed in [4].

P. S. M. Kop Jansen

Papers

Upper Triangularization Of Matrices By Lower Triangular Similarities

Upper triangularization of matrices by lower triangular similarities