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2007•Journal of Shanghai Normal UniversityRequires access

The existence of the generalized inverse A_(T,S)~((2)) of a matrix A over skew fields

Guorong Wang

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Abstract

We discuss further the generalized inverse A(2)T,S of a matrix A over skew fields,give a necessary and sufficient condition for the existence of A(2)T,S,and verify that the group inverse,the Drazin inverse and the ρ Moore-Penrose inverse are identical with A(2)R(G),N(G) for a suitable matrix G,respectively.

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What this paper is about

We discuss further the generalized inverse A(2)T,S of a matrix A over skew fields,give a necessary and sufficient condition for the existence of A(2)T,S,and verify that the group inverse,the Drazin inverse and the ρ Moore-Penrose inverse are identical with A(2)R(G),N(G) for a suitable matrix G,respectively.

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Available abstract

We discuss further the generalized inverse A(2)T,S of a matrix A over skew fields,give a necessary and sufficient condition for the existence of A(2)T,S,and verify that the group inverse,the Drazin inverse and the ρ Moore-Penrose inverse are identical with A(2)R(G),N(G) for a suitable matrix G,respectively.

Key concepts: Inverse, Mathematics, Drazin inverse, Skew, Matrix (chemical analysis), Generalized inverse, Moore–Penrose pseudoinverse, Pure mathematics

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