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
收藏
页码：2091 / 2109
页数：19
相关论文
共 26 条
  • [1] Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute (vol 437, pg 2091, 2012)
    Kisi, Emre
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 477 : 211 - 212
  • [2] On idempotency and tripotency of linear combinations of two commuting tripotent matrices
    Ozdemir, Halim
    Sarduvan, Murat
    Ozban, Ahmet Yasar
    Guler, Nesrin
    APPLIED MATHEMATICS AND COMPUTATION, 2009, 207 (01) : 197 - 201
  • [3] Notes on linear combinations of two tripotent, idempotent, and involutive matrices that commute
    Ozdemir, Halim
    Sarduvan, Murat
    ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2008, 16 (02): : 83 - 89
  • [4] When is a linear combination of two idempotent matrices the group involutory matrix?
    Baksalary, Jerzy K.
    Baksalary, Oskar Maria
    LINEAR & MULTILINEAR ALGEBRA, 2006, 54 (06): : 429 - 435
  • [5] k-Idempotency of linear combinations of an idempotent matrix and a tripotent matrix that commute
    S. Krishnamoorthy
    T. Rajagopalan
    Indian Journal of Pure and Applied Mathematics, 2011, 42 : 99 - 108
  • [6] k-IDEMPOTENCY OF LINEAR COMBINATIONS OF AN IDEMPOTENT MATRIX AND A TRIPOTENT MATRIX THAT COMMUTE
    Krishnamoorthy, S.
    Rajagopalan, T.
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2011, 42 (02): : 99 - 108
  • [7] A Note on Linear Combinations of Two Tripotent Matrices
    Kou, Yanli
    Cao, Chongguang
    ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL 1: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS, 2008, : 99 - 102
  • [8] On linear combinations of two tripotent, idempotent, and involutive matrices
    Sarduvan, Murat
    Ozdemir, Halim
    APPLIED MATHEMATICS AND COMPUTATION, 2008, 200 (01) : 401 - 406
  • [9] On the spectrum of linear combinations of finitely many diagonalizable matrices that mutually commute
    Kisi, Emre
    Sarduvan, Murat
    Ozdemir, Halim
    Kalayci, Nurgul
    SPECIAL MATRICES, 2021, 9 (01): : 305 - 320
  • [10] The Group Involutory Matrix of the Combinations of Two Idempotent Matrices
    Wu, Lingling
    Liu, Xiaoji
    Yu, Yaoming
    JOURNAL OF APPLIED MATHEMATICS, 2012,
123