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

Authors

Matthew He, Nova Southeastern UniversityFollow
Paolo E. Ricci, Università di Roma “La Sapienza”

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 R_λ(A) of a complex r×r matrix A is an analytic function in any domain with empty intersection with the spectrum Σ_A of A. The well known Taylor expansion of R_λ(A) in a neighborhood of any given λ₀∉Σ_A is modified taking into account that only the first powers of R_λ0(A) are linearly independent. The main tool in this framework is given by the multivariable polynomials depending on the invariants v₁,v₂,…,v_r of R_λ(A) (m denotes the degree of the minimal polynomial). These functions are used in order to represent the coefficients of the subsequent powers of R_λ0(A) as a linear combination of the first m of them.

NSUWorks Citation

He, Matthew and Ricci, Paolo E., "On Taylor’s Formula for the Resolvent of a Complex Matrix" (2008). Mathematics Faculty Articles. 161.
https://nsuworks.nova.edu/math_facarticles/161

DOI

10.1016/j.camwa.2008.03.051