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广义逆A_(T,S)^(2)的几种等价表示式及其应用 被引量:2

Some equivalent representations of generalized inverse A_(T,S)^((2)) and its application
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摘要 给出了广义逆A_(A,S)^(2)的一种新的表示式,推广了Zlobec公式,证明了广义逆A_(T,S)^(2)的4种表示式子间的等价关系,并给出了它的应用。 A new representation of the generalized inverse AT,S^(2) is given. We generalize the Zlobec' formula in [3,4 ], prove the equivalence of four representations of the generalized inverse a AT,S^(2), and give its application.
作者 孙劼 王国荣
出处 《上海师范大学学报(自然科学版)》 2005年第4期8-12,共5页 Journal of Shanghai Normal University(Natural Sciences)
基金 上海市教委科技发展基金(050Z07 03DZ04)
关键词 广义逆AT S^(2) 等价关系 Zlobec公式 generalized inverse AT,S^(2) equivalence Zlobec' formula
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参考文献6

  • 1WEI Y M.A characterization and representation of the generalized inverse A(2)T,S and its applications[ J ].Linear Algebra Appl,1998,280:87-96.
  • 2MIAO J M,BEN-ISRAEL.A minors of the Moore-Penrose inverse[ J ].Linear Algebra Appl.,195 (1993):191-207.
  • 3ZLOBEC S.An explicit form of the Moore-Penrose inverse of an arbitrary complex matrix[ J ].SIAM Review,1970,12:132-134.
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同被引文献15

  • 1何旭初 孙文瑜.广义逆矩阵引论[M].南京:江苏科学技术出版社,1990..
  • 2Marsaglia G, Styan G P H. Equalities and inequalities for ranks of matrices [J]. Linear and Multilinear Algebra, 1974, 2:269-292.
  • 3Tian Y G. How to characterize equalities for the Moore-Penrose inverse of a matrix [J], Kyungpook Mathematical Journal, 2001, 41:1-15.
  • 4Tian Y G. More on maximal and minimal ranks of Schur complements with applications [J]. Appl. Math. Comput., 2004, 152:675-692
  • 5Tian Y G. Rank equalities related to outer invrese of matrices and applications [J]. Linear and Multilinear Algebra, 2001, 49:269-288.
  • 6Liu Y H, WEI M S. Rank equalities related to the generalized inverse AT,S^(2) and BT1,S1^(2) of two matrices A and B [J]. Appl. Math. Comput., 2004, 159:19-28.
  • 7Wang G R, Wei Y M, Qiao S Z. Generalized Inverses: Theory and Computations [M]. Beijing:Science Press, 2004.
  • 8Ben-Israel A, Greville T N E. Generalized Inverses: Theory and Applications [M]. New York: John Wiley, 1974.
  • 9Wei Y M. A characterization and representation of the generalized inverse AT,S^(2) and its applications [J]. T,S Linear Alg. Appl., 1998, 280:87-96.
  • 10Chen Y L. A Cramer rule for solution of the general restricted linear equations [J].Linear and Multilinear Algebra, 1993, 34:177-186.

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