期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

Some Rank Equalities about Combinations of Two Idempotent Matrices 被引量：1

Some Rank Equalities about Combinations of Two Idempotent Matrices
原文传递
导出
摘要 The paper researches the rank of combinations a PA＋bAQ-cPAQ of two idempotent matrices P and Q.Using the properties of the idempotent matrix and elementary block matrix operation,we get some rank equalities for combinations a PA＋bAQ-cPAQ of two idempotent matrices P and Q.These rank equalities generalize the results of Koliha J J,Rakoevi V and Tian Y,and give some applications of the rank equalities. The paper researches the rank of combinations a PA＋bAQ-cPAQ of two idempotent matrices P and Q.Using the properties of the idempotent matrix and elementary block matrix operation,we get some rank equalities for combinations a PA＋bAQ-cPAQ of two idempotent matrices P and Q.These rank equalities generalize the results of Koliha J J,Rakoevi V and Tian Y,and give some applications of the rank equalities.
作者 ZUO Kezheng
机构地区 School of Mathematics and Statistics
出处 《Wuhan University Journal of Natural Sciences》 CAS 2010年第5期380-384,共5页 武汉大学学报（自然科学英文版）
关键词 idempotent matrix RANK INVERTIBILITY RANGE null space idempotent matrix rank invertibility range null space
分类号 O151.2 [理学—基础数学]
  • 相关文献

参考文献2

二级参考文献11

  • 1Baksalary J. K. , Baksalary O. M.. Nonsingularity of Linear combinations of idempotent matrices[J]. Linear Algebra Appl. , 2004,388:25-29.
  • 2Groβ J. , Trenkler G.. Nonsingularity of the difference of two oblique projectors[J]. SIAM J. Matrix Anal. Appl. , 1999,21:390-395.
  • 3Koliha J. J. , Rakoceic V.. The nullity and rank of linear combinations of idempotent matrices[J]. Linear Algebra Appl. , 2006,418 : 11-14.
  • 4Koliha J. J. , Rakoceic V. , I. Straskraba.. The difference and sum of projectors[J]. Linear Algebra Appl. , 2004, 388:279-288.
  • 5Marsaglia G. , styan G. P. H.. Equalities and inequalities for the rank of matrices[J]. Linear and Mutilinear Algebra. , 1974, 2:269-292.
  • 6Gross J.,Trenkler G..Nonsingularity of the difference of two obligue projectors[J].SIAM J.Matrix Anal.Appl.1999,21(2):390-395.
  • 7Koliha J.J..Rakoevic V.Invertibility of the sum of idempotents[J].Linear Multil.Algebra,2002,50(4):285-292.
  • 8Koliha J.J.,Rakoevic V..Invertibility of the difference of idempotents[J].Linear Multil.Algebra,2003,51(1):97-100.
  • 9Rakocevic V..On the norm of idempotents in a Hilbert space[J].Amer.Math.Monthly,2000,107(8):748-750.
  • 10Wimmer H.K..Canonical angles of unitary spaces and perturbations of direct complements[J].Linear Alg.Appl.1999,287(3):373-379.

共引文献13

同被引文献12

  • 1TIAN Y’STYAN G P H. Rank equalities for idempotent matrices with applications[J]. Journal of Computational and AppliedMathematics, 2006,191:7-97.
  • 2GROfi J ,TRENKLER G. Nonsingularity of the difference of two oblique projectors[J]. SIAM J Matrix Anal Appl, 2000, 21 :390-395.
  • 3BAKSALARY J K, BAKSALARY O M. Nonsingularity of linear combinations of idempotent matrices [J]. Linear AlgebraAppl,2004,388:25-29.
  • 4TIAN Y’STYAN G P H. Rank equalities for idempotent and involutory matrices [J]. Linear Algebra and Its Applications,2001,335:101-117.
  • 5TIAN Y. Rank equalities related to generalized Inverses of matrices and their applications[DB/OL]. [2011-08-06]. http://arxiv. org/abs math/0003224vl,2000-03-30:17-25.
  • 6MIKHAIL A CHEBOTAR, WEN-FONG KE,PJEK-HWEE LEE,et al. On maps preserving zero jordan products[J]. MonatshMath,2006,149:91-101.
  • 7FAREBROTHER R W, TRENKLER G. On generalized quadratic matrices[J]. Linear Algebra and Its Applications,2005,410:244-253.
  • 8HWA-LONG GAU, CHIH-JEN WANG, NGAI-CHING WONG. Invertibility and fredholmness of linear combinations ofquadratic,^-potent and nilpotent operators[J]. Operators and Matrices,2008,2(2) : 193-199.
  • 9TIAN Y,STYAN G P H. When does rank (ABC) = rank(AB) + rank(BC) — rank(B) hold? [J]. International Journal ofMathematical Education in Science and Technology ,2002 ,33 : 127-137.
  • 10KOLIHA J J,RAKOCEVIC V,STRASKRABA I. The difference and sum of projectors[J]. Linear Algebra Appl, 2004,388 :279-288.

引证文献1

二级引证文献3

Wuhan University Journal of Natural Sciences
2010年 第5期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部