IJPAM: Volume 108, No. 4 (2016)

EXPLICIT MINIMUM POLYNOMIAL, EIGENVECTOR, AND
INVERSE FORMULA FOR NONSYMMETRIC
ARROWHEAD MATRIX

Wiwat Wanicharpichat
$^1$Department of Mathematics
Faculty of Science
and
$^2$Research Center for Academic Excellence in Mathematics
Naresuan University
Phitsanulok 65000, THAILAND


Abstract. In this paper, we treat the eigenvalue problem for a nonsymmetric arrowhead matrix which is the general form of a symmetric arrowhead matrix. The purpose of this paper is to present explicit formula of determinant, inverse, minimum polynomial, and eigenvector formula of some nonsymmetric arrowhead matrices are presented.

Received: June 6, 2016

AMS Subject Classification: 15A09, 15A15, 15A18, 15A23, 65F15, 65F40

Key Words and Phrases: arrowhead matrix, Krylov matrix, Schur complement, nonderogatory matrix

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DOI: 10.12732/ijpam.v108i4.21 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 4
Pages: 967 - 984


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