The uniqueness of expression for generalized quadratic matrices

被引：0
|
作者：
Chen, Meixiang [1 ]
Yang, Zhongpeng [2 ]
Chen, Qinghua [3 ]
机构：
[1] Putian Univ, Fujian Key Lab Financial Informat Proc, Putian 351100, Fujian, Peoples R China
[2] Putian Univ, Fujian Prov Univ, Key Lab Appl Math, Putian 351100, Fujian, Peoples R China
[3] Fujian Normal Univ, Sch Math & Stat, Fuzhou 350007, Fujian, Peoples R China
来源：
OPEN MATHEMATICS | 2024年 / 22卷 / 01期
基金：
中国国家自然科学基金;
关键词：
generalized quadratic matrix; uniqueness; linear combination; rank; LINEAR-COMBINATIONS; RANK EQUALITIES; IDEMPOTENT; SPECTRA;
D O I：
10.1515/math-2023-0186
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that the expression as A(2) = alpha A + beta P for generalized quadratic matrices is not unique by numerical examples. Then it is proven that the uniqueness of expression for generalized quadratic matrices is concerned not only with the properties of A but also with the rank of P . Furthermore, the sufficient and necessary conditions for the uniqueness of generalized quadratic matrices'expression are obtained. Finally, some related discussions about generalized quadratic matrices are also given.
引用
收藏
页数：14
相关论文
共 50 条
  • [1] On generalized quadratic matrices
    Farebrother, RW
    Trenkler, G
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 410 : 244 - 253
  • [2] NATURE OF LACK OF UNIQUENESS OF GENERALIZED INVERSE MATRICES
    URQUHART, NS
    SIAM REVIEW, 1969, 11 (02) : 268 - &
  • [3] Generalized quadraticity of linear combination of two generalized quadratic matrices
    Petik, T.
    Uc, M.
    Ozdemir, H.
    LINEAR & MULTILINEAR ALGEBRA, 2015, 63 (12): : 2430 - 2439
  • [4] Rank equalities for commutator of generalized quadratic matrices and their applications
    Yang, Z. (yangzhongpeng@126.com), 2013, CESER Publications, Post Box No. 113, Roorkee, 247667, India (32):
  • [5] On the spectra of some combinations of two generalized quadratic matrices
    Petik, Tugba
    Ozdemir, Halim
    Benitez, Julio
    APPLIED MATHEMATICS AND COMPUTATION, 2015, 268 : 978 - 990
  • [6] Rank equalities for commutator of generalized quadratic matrices and their applications
    Lv, Hongbin
    Yang, Zhongpeng
    Chen, Meixiang
    INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2013, 32 (02): : 59 - 67
  • [7] The generalized quadraticity of linear combinations of two commuting quadratic matrices
    Uc, Mahmut
    Petik, Tugba
    Ozdemir, Halim
    LINEAR & MULTILINEAR ALGEBRA, 2016, 64 (09): : 1696 - 1715
  • [8] The Solution of Inverse Quadratic Eigenvalue Problem for Generalized Centrosymmetric Matrices
    Wang, Xiangrong
    ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL 1: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS, 2008, : 289 - 292
  • [9] Invariance of rank and nullity for linear combinations of sum and product of generalized quadratic matrices
    Liu, Shuyuan
    Chen, Meixiang
    Feng, Xiaoxia
    Yang, Zhongpeng
    Xie, Yanping
    International Journal of Applied Mathematics and Statistics, 2013, 42 (12): : 157 - 166
  • [10] Invariance of Rank and Nullity for Linear Combinations of Sum and Product of Generalized Quadratic Matrices
    Liu, Shuyuan
    Chen, Meixiang
    Feng, Xiaoxia
    Yang, Zhongpeng
    Xie, Yanping
    INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2013, 42 (12): : 157 - 166
12345