Document Type

Article

Publication Date

6-2010

Publication Title

Alexandria Journal of Mathematics

ISSN

2090‐4789

Abstract

Linear matrix pencil, denoted by (A,B), plays an important role in control systems and numerical linear algebra. The problem of finding the eigenvalues of (A,B) is often solved numerically by using the well-known QZ method. Another approach for exploring the eigenvalues of (A,B) is by way of its characteristic polynomial, P(λ)=A − λB. There are other applications of working directly with the characteristic polynomial, for instance, using Routh-Hurwitz analysis to count the stable roots of P(λ) and transfer function representation of control systems governed by differential-algebraic equations. In this paper, we present an algorithm for algebraic construction of the characteristic polynomial of a regular linear pencil. The main theorem reveals a connection between the coefficients of P(λ) and a lexicographic combination of the rows between matrices A and B.

Comments

This article was retrieved from the Alexandria Journal of Mathematics, which is an open access journal.

Open Access authors retain the copyrights of their papers, and all open access articles are distributed under the terms of the Creative Commons Attribution license, which permits unrestricted use, distribution and reproduction in any medium, provided that the original work is properly cited.

Included in

Mathematics Commons

Share

COinS