关于算子乘积的一类逆序律

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摘要利用算子分块矩阵的技巧,研究了两个算子乘积的{1,3}-逆的逆序律,给出了闭值域有界线性算子的{1,3}-逆的矩阵表示,证明了当R(A),R(B)和R(AB)都闭时,B{1,3}A{1,3} ■ AB{1,3},{B;(ABB^(13))^(13)}■{(AB)^(13)}成立的充分必要条件。

作者王洁

机构地区运城师范高等专科学校

出处《江西电力职业技术学院学报》 CAS 2022年第2期50-52,54,共4页 Journal of Jiangxi Vocational and Technical College of Electricity

关键词广义逆分块算子矩阵

参考文献2

1Baksalary J K, Kala R. Range invariance of certain matrix products. Linear and Multilinear Algebra, 1983, 14: 89-96.
2Baksalary J K, Markiewicz A. Further results on invariance of the eigenvalues of matrix products involving generalized inverses. Linear Algebra Appl., 1996, 237-238: 115-121.
3Baksalary J K, Mathew T. Rank invariance criterion and its application to the unified theory of least squares. Linear Algebra Appl., 1990, 127: 393-401.
4Baksalary J K, Pukkila T. A note on invariance of the eigenvalues, singular values, and norms of matrix products involving generalized inverses. Linear Algebra Appl., 1992, 165: 121-130.
5Baksalary J K, Puntanen S. Spectrum and trace invariance criterion and its statistical applications. Linear Algebra Appl., 1990, 142: 121-128.
6Groβ J and Tian Y. Invariance properties of a triple matrix product involving generalized inverses. Linear Algebra Appl., 2006, 417: 94-107.
7Tian Y. Upper and lower bounds for ranks of matrix expressions using generalized inverses. Linear Algebra Appl., 2002, 355: 187-214.
8Tian Y. More on maximal and minimal ranks of Schur complements with applications. Appl. Math. Comput., 2004, 152: 675-692.
9Tian Y, Cheng S. The maximal and minimal ranks of A - BXC with applications. New York J. Math., 2003, 9: 345-362.
10Penrose R. A generalized inverse for matrices. Proc. Cambridge Philos. Soc., Cambridge, 1955, 51: 406-413.

江西电力职业技术学院学报

2022年第2期

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