用有边矩阵刻画广义逆

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 1980-10-01 DOI:10.1016/0024-3795(80)90093-2

Kentaro Nomakuchi

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引用次数: 11

摘要

考虑了一种刻画任意给定矩阵A的所有广义逆类的方法。给定一个矩阵a和a的非奇异有边矩阵T, T=APQR，则T-1对应的子矩阵a是a的广义逆，反过来，可以用该方法求出a的任何广义逆。广义逆有不同的定义，这些论证都是用限制最少的定义来展开的。Moore-Penrose逆(最严格的定义)的表征也被考虑。

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On the characterization of generalized inverses by bordered matrices

A method to characterize the class of all generalized inverses of any given matrix A is considered. Given a matrix A and a nonsingular bordered matrix T of A, $T= A P Q R$ the submatrix, corresponding to A, of T^-1 is a generalized inverse of A, and conversely, any generalized inverse of A is obtainable by this method. There are different definitions of a generalized inverse, and the arguments are developed with the least restrictive definition. The characterization of the Moore-Penrose inverse, the most restrictive definition, is also considered.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.