2011•Journal of Huzhou Teachers CollegeRequires access

The Group Inverse of Two Classes of Block Matrix

Feng Mao-chun

Abstract

When P is singular idempotent matrix,using the properties of matrixes rank,elementary transformation of block matrix,and necessary and sufficient condition for the existence of group inverse,we discuss the existence of group inverse of block matrix shaped likeM=P P+PP* P 0and M=P P P+PP* 0(P is square matrix).Next,using elementary transformation and calculation method for 1 inverse of matrix,according to the relation of matrices' group inverses and 1 inverse of 3 power of matrix.Finally we give the general expression of the two kind of block matrixes' group inverse,and illustrate it with examples.

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Key concepts: Mathematics, Inverse, Block matrix, Idempotent matrix, Involutory matrix, Group (periodic table), Matrix (chemical analysis), Square root of a 2 by 2 matrix