Mathematics Faculty Articles

Title

On Taylor’s Formula for the Resolvent of a Complex Matrix

Document Type

Article

Publication Date

11-1-2008

Publication Title

Computers & Mathematics with Applications

Keywords

Powers of a matrix, Matrix invariants, Resolvent

ISSN

0898-1221

Volume

56

Issue/No.

9

First Page

2285

Last Page

2288

Abstract

The resolvent Rλ(A) of a complex r×r matrix A is an analytic function in any domain with empty intersection with the spectrum ΣA of A. The well known Taylor expansion of Rλ(A) in a neighborhood of any given λ0∉ΣA is modified taking into account that only the first powers of Rλ0(A) are linearly independent. The main tool in this framework is given by the multivariable polynomials depending on the invariants v1,v2,…,vr of Rλ(A) (m denotes the degree of the minimal polynomial). These functions are used in order to represent the coefficients of the subsequent powers of Rλ0(A) as a linear combination of the first m of them.

DOI

10.1016/j.camwa.2008.03.051

This document is currently not available here.

Peer Reviewed

Find in your library

Share

COinS