# IJPAM: Volume 109, No. 4 (2016)

**EXPLICIT MOORE-PENROSE INVERSE AND**

GROUP INVERSE OF DOUBLY LESLIE MATRIX

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

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

where , , and is a diagonal matrix of order . The matrix 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**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2016

**Volume:**109

**Issue:**4

**Pages:**959 - 974

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**This work is licensed under the Creative Commons Attribution International License (CC BY).**