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关于3个幂等矩阵线性组合的若干探讨 被引量：6

Some studies about linear combinations of three idempotent matrices
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摘要 目的研究当P1,P2,P3是3个非零的两两相互可交换的n×n幂等矩阵并且c1,c2,c3是非零复数时,矩阵c1P1+c2P2+c3P3是幂等矩阵所必须满足的条件。方法使用归纳的方法进行总结。结果找到了c1P1+c2P2+c3P3是幂等矩阵的一些充分条件与P1+P2+P3是幂等矩阵的一个充要条件。结论丰富了幂等矩阵线性组合研究的相关理论。 Aim To study some conditions when the matrix c1P1 ＋c2P2 ＋c3P3 is an idempotent matrix where P1, P2 and P3 are any three nonzero mutually commutative n×n idempotent matrices and c1, c2 and c3 are nonzero scalars. Methods The induction method is used to find the results. Results Some sufficient conditions for the matrix c1P1 ＋c2P2 ＋c3P3 to be an idempotent matrix are given and a necessary and sufficient condition for the matrix P1 ＋P2 ＋P3 is given too. Conclusion The results furnish the related theory of linear combinations of idempotent matrices.
作者 谢涛
机构地区 湖北师范学院数学与统计学院
出处 《宝鸡文理学院学报（自然科学版）》 CAS 2010年第1期11-13,共3页 Journal of Baoji University of Arts and Sciences(Natural Science Edition)
基金 湖北师范学院研究生启动项目(2007D52)
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]
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参考文献7

  • 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, STYAN G P H. Idempotency of linear combinations of an idempotent matrix and a tripotent matrix [J ]. Linear Algebra Appl, 2002, 354:414-418.
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  • 6OZDEMIR H, OZBAN A Y. On idempotency of linear combinations of idempotent matrices [J]. Applied Mathematics and Computation, 2004, 159:439-448.
  • 7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

二级参考文献3

  • 1BAKSALARY, 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.
  • 2HALIM OZDEMIR, AHRNET YASAR OZBAN.On idempotency of linear combinations of idempotent matrices[J ]. Applied Mathematics and Computation, 2004, 159 (2) : 439-448.
  • 3RABANOVICH 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52

  • 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
  • 2RABANOVICH V. Every matrix is a linear combination of three idempotents [J]. Linear Algebra Appl, 2004, 390: 137-14.
  • 3PEARCY C, TOPPING D. Sums of small numbers of idempotents[J]. Michigan J Math, 1967, 14: 453-465.
  • 4BAKSALARY J K. BAKSALARY O M. Nonsingularity of linear combinations of idempotent matrices[J]. Linear Algebra Appl, 2004, 388: 25-29.
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  • 6DU Hong-ke, YAO Xi-yan, DENG Chun-yan. Invertibility of linear combinations of two idempotents [J]. Pro Amer Math Soc, 2006, 134: 1451-1457.
  • 7KOLIHA J J, RAKOCEVIC V. Stability theorems for linear combinations of idempotents[J]. Integr Equ Oper Theory, 2007, 58 : 597-601.
  • 8WU Pei-yuan. Sums of idempotent matrices[J]. Linear Algebra Appl, 1990, 142: 43-54.
  • 9GAU H L, WANG C J, WONG N C. Invertibility and Fredholmness of linear combinations of quadratic, k-potent and nilpotent operators[J]. Operators and Matrices, 2008,2 : 193-199.
  • 10Baksalary J K, Baksalary O M. Idemoptency of linear combinations of three idempotent matrices [ J ]. Linear Algebra Appl, 2000, 321:3-7.

引证文献6

二级引证文献7

宝鸡文理学院学报（自然科学版）
2010年 第1期

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