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四个幂等矩阵线性组合的幂等性 被引量：3

Idempotency of linear combinations of four idempotent matrices
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摘要 给出了当P1,P2,P3,P4是四个不同的非零的两两可交换的n×n幂等矩阵并且c1,c2,c3,c4是非零复数时,线性组合c1P1+c2P2+c3P3+c4P4在两两乘积等于零与两两乘积等于其中一个的条件下仍是幂等矩阵的一些充要条件. Let P1,P2,P3,P4 be any four different nonzero mutually commutatiove idempotent matrices and c1,c2,c3,c4 be nonzero scalars.In the present note,some sufficient conditions for the matrix c1P1＋c2P2＋c3P3＋c4P4 to be an idempotent matrix are given under the condition that the mutual product is zero or the mutual product is equal to the either one.
作者 谢涛
机构地区 湖北师范学院数学与统计学院
出处 《湖北师范学院学报（自然科学版）》 2010年第4期15-18,共4页 Journal of Hubei Normal University(Natural Science)
基金 湖北师范学院教研项目(2008D56)
关键词 幂等矩阵 特征值 线性组合 idempotent matrix Characteristic Value linear combination
分类号 O177.91 [理学—基础数学]
  • 相关文献

参考文献9

  • 1Baksalary J K, Baksalary O M. Idemoptency of linear combinations of three idempotent matrices [ J ]. Linear Algebra Appl, 2000, 321:3-7.
  • 2Baksalary O M. Idemopteney of linear combinations of three idempotent matrices, two of which are disjoint [ J ]. Linear Algebra Appl, 2004, 388:67 - 78.
  • 3Baksalary J K, Baksalary O M, Sty. an G P H. Idempotency of hnear combinations of an idempotent matrix and a tripotent matrix[J]. Linear Algebra Appl, 2002, 354:414 -418.
  • 4Benitez J, Thome N. Idempotency of linear combinations of an idempotent matrix and t- potent matrix that commute[J]. Linear Algebra Appl, 2004, 403:414 - 418.
  • 5Baksalary O M, Benitez J. Idemoptency of linear combinations of three idempotent matrices, two of which are commuting [ J]. Linear Algebra Appl, 2007, 424:320 - 337.
  • 6Hom R A, Johnson C R. Matrices analysis [M]. Cambridge: Cambridge University Press, 1991.
  • 7Ozdemir H, Ozban A Y. On idempotency of linear combinations of idempotent matrices [J].Applied Mathematics and Computation, 2004, 159:439 -448.
  • 8王月清,王爱丽.3个幂等矩阵线性组合的幂等性[J].宝鸡文理学院学报（自然科学版）,2005,25(3):167-168. 被引量：7
  • 9谢涛.关于3个幂等矩阵线性组合的若干探讨[J].宝鸡文理学院学报（自然科学版）,2010,30(1):11-13. 被引量：6

二级参考文献10

  • 1王月清,王爱丽.3个幂等矩阵线性组合的幂等性[J].宝鸡文理学院学报（自然科学版）,2005,25(3):167-168. 被引量：7
  • 2BAKSALARY J K, BAKSALARY O M. Idemoptency of linear combinations of three idempotent matrices [J]. Linear Algebra Appl, 2000, 321:3-7.
  • 3BAKSALARY O M. Idemopteney of linear combinations of three idempotent matrices, two of which are disjoint [J]. Linear Algebra Appl, 2004, 388: 67-78.
  • 4BAKSALARY J K, BAKSALARY O M, STYAN G P H. Idempotency of linear combinations of an idempotent matrix and a tripotent matrix [J ]. Linear Algebra Appl, 2002, 354:414-418.
  • 5BENITEZ J, THOME N. Idempoteney of linear combinations of an idempotent matrix and t - potent matrix that commute [J]. Linear Algebra Appl, 2004, 403:414-418.
  • 6HORN R A, JOHNSON C R. Matrices analysis [M]. Cambridge: Cambridge University Press, 1991.
  • 7OZDEMIR H, OZBAN A Y. On idempotency of linear combinations of idempotent matrices [J]. Applied Mathematics and Computation, 2004, 159:439-448.
  • 8BAKSALARY, OSKAR MARIA. Idempotency of linear combinations of three idempotent matrices,two of which are disjoint[J]. Linear Algebra and its Applications , 2004, 388 : 67-78.
  • 9HALIM OZDEMIR, AHRNET YASAR OZBAN.On idempotency of linear combinations of idempotent matrices[J ]. Applied Mathematics and Computation, 2004, 159 (2) : 439-448.
  • 10RABANOVICH V. Every matrix is a linear combination of three idempotents[J]. Linear Algebra and its Applications, 2004, 390:137-143.

共引文献6

同被引文献28

  • 1王月清,王爱丽.3个幂等矩阵线性组合的幂等性[J].宝鸡文理学院学报（自然科学版）,2005,25(3):167-168. 被引量：7
  • 2Baksalary J K, Baksalary 0 M. Idemoptency of linearcombinations of three idempotent matrices [J]. Linear Algebra Appl, 2000, 321:3-7.
  • 3Baksalary O M. ldemoptency of linear combinations of three idempotent matrices, two of which are disjoint [J]. Linear Algebra Appl, 2004, 388 : 67-68.
  • 4Baksalary J K, Baksalary O M, Styan G P H. Idemop- tency of linear combinations of an idempotent matrix and a tripotent matrix [J]. Linear Algebra Appl, 2002, 354:414-418.
  • 5Benitez J, Thome N. Idemoptency of linear combina- tions of an idempotent matrix and t-potent matrix and commute [J]. Linear Algebra Appl, 2004, 403: 414-418.
  • 6Baksalary O M, Benitez J. Idemoptency of linear combi- nations of three idempotent matrices, two of which are commuting [J]. Linear Algebra Appl, 2007, 424: 320-337.
  • 7Horn R A, Johnson C R. Matrices analysis [M]. Cam- bridge: Cambridge University Press, 1991.
  • 8Ozdemir H, Ozban A Y. On idempotency of linear com- binations of idempotent matrices[J]. Applied Mathemat- ics and Computation, 2004, 159:439-448.
  • 9Baksalary J K,Baksalary O M.Idemoptency of linear combinations of three idempotent matrices[J].Linear Algebra Appl,2000,321:3-7.
  • 10Baksalary O M.Idemoptency of linear combinations of three idempotent matrices,two of which are disjoint[J].Linear Algebra Appl,2004,388:67-68.

引证文献3

二级引证文献2

湖北师范学院学报（自然科学版）
2010年 第4期

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