Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute

被引：13

作者：

Xu, Chuang ^{[1
,2
,3
]}

Xu, Runzhang ^{[1
]}

机构：

[1] Harbin Engn Univ, Coll Sci, Harbin 150001, Peoples R China

[2] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[3] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 437卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Tripotent matrix; Involutory matrix; ldempotent matrix; Partitioned blocks; Commutativity; T-POTENT MATRIX; IDEMPOTENT MATRICES;

D O I：

10.1016/j.laa.2012.05.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper concerns with the tripotency of a linear combination of three matrices, which has a background in statistical theory. We demonstrate all the possible cases that lead to the tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute. By utilizing block technique and returning the partitioned matrices to their original forms, we derive the sufficient and necessary conditions such that a linear combination of three mutually commuting involutory matrices is tripotent. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：2091 / 2109

页数：19

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