Pseudo-Inverses in Associative Rings and Semigroups
Pseudo-Inverses in Associative Rings and Semigroups
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DOI：
10.1080/00029890.1958.11991949
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发表时间：
1958-08
影响因子：
0.5
通讯作者：
M. Drazin
中科院分区：
文献类型：
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作者：
M. Drazin
1.引言。Eh Moore([5]，参见此外，PenRose[6]，Rado[8])已经证明了，给定复数域中元素的任意方阵x，当x-1恰好存在时，定义另一个矩阵是可能的，并且具有(即使对于奇异x)导致几个定理的简单证明的性质，这些定理只有在困难(如果有的话)的情况下才能得到其他方法。更准确地说，摩尔的结果(以彭罗斯的形式表示)是，给定任意平方*复矩阵x，则总有一个复矩阵c满足
1. Introduction. EH Moore ([5], and cf. also Penrose [6], Rado [8]) has shown how, given any square matrix x with elements in the complex field, it is possible to define another matrix, coinciding with x-1 whenever x-1 happens to exist, and having (even for singular x) properties leading to simple proofs of several theorems which yield to other methods only with difficulty (if at all). More precisely, Moore's result (stated in Penrose's form) is that, given any square* complex matrix x, then there is always exactly one complex matrix c satisfying