IJPAM: Volume 109, No. 4 (2016)

EXPLICIT MOORE-PENROSE INVERSE AND
GROUP INVERSE OF DOUBLY LESLIE MATRIX

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

Abstract. A doubly Leslie matrix is a bordered real matrix of the form

\begin{displaymath}L=\left[ \begin{array}{cc} -\mathbf{p}^{T} & -a_{n}-b_{n} \\ \Lambda & -\mathbf{q} \end{array}\right] _{(n,n)},\end{displaymath}

where $a_{n}, b_{n} \in \mathbb{R}$, $\mathbf{p}, \mathbf{q} \in \mathbb{R}^{n-1}$, and $\Lambda = \operatorname{diag}(s_{1}, s_{2}, \dots, s_{n-1})$ is a diagonal matrix of order $n-1$. The matrix $L$ is a closed form of a doubly companion matrix, a Leslie matrix and a companion matrix. This paper is discussed the explicit formula of the Moore-Penrose inverse and the group inverse of the doubly leslie matrix. In general the Moore-Penrose inverse of a rectangle doubly Leslie matrix is also discussed.

Received: August 19, 2016

Revised: September 14, 2016

Published: October 9, 2016

AMS Subject Classification: 15A09, 15A23

Key Words and Phrases: companion matrix, doubly companion matrix, Leslie matrix, doubly Leslie matrix, Moore-Penrose inverse, group inverse
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DOI: 10.12732/ijpam.v109i4.17 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: 109
Issue: 4
Pages: 959 - 974


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