广义逆矩阵类的一个特性 |
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引用本文: | 周士藩.广义逆矩阵类的一个特性[J].赣南师范学院学报,1987(Z1). |
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作者姓名: | 周士藩 |
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作者单位: | 苏州大学数学系 |
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摘 要: | 众所周知,每一非奇异矩阵A有唯一的逆矩阵,通常记为A~(-1),并且,若A~(-1)=B~(-1),则A=B。类似地,设An{i、j、…、k)是已知矩阵A_n的一个广义逆类(n=1、2),并且若A_1{i,j、…、k}=A_2{i、j、…、k}(i、j、…,k∈{1、2、3、4、5})。那么,A_1=A_2吗? 在这篇文章中,我们解决上述这些问题。
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A Characterization of Generalized Inverse Class of Matrices |
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Abstract: | It is well-known that every nonsingular matrix A has a unique inverse, usually denoted by A-1, and if A-1-B-1, then A = B. Analogously,let An { i,j…,k } be a class of generalized inverse of a given matrix An ( n = l,2 ) ,and A1 { i,j,…?k } = A2 { i,j,…,k } ( i,j,…?k∈ {1,2,3,4, 5 } ) . Does A1 = A2 hold?
In this paper, we solved the problems as indicated above. |
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