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2009•Journal of MathematicsRequires access

NEW REPRESENTATIONS FOR GROUP INVERSE AND DRAZIN INVERSE WITH THEIR APPLICATIONS

Jing Cai

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Abstract

In this paper, we study the condition for the existence of group inverse, representations of group inverse and Drazin inverse and their computations. A sufficient and necessary condition for the existence of group inverse is given by means of determinantal representation. New representation of group inverse is also presented in terms of original matrix’s maximal nonsingular submatrix. Based on this, we generalize the results to Drazin inverse. Thus we propose a new method to calculate group inverse and Drazin inverse.

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What this paper is about

In this paper, we study the condition for the existence of group inverse, representations of group inverse and Drazin inverse and their computations. A sufficient and necessary condition for the existence of group inverse is given by means of determinantal representation. New representation of group inverse is also presented in terms of original matrix’s maximal nonsingular submatrix. Based on this, we generalize the results to Drazin inverse. Thus we propose a new method to calculate group inverse and Drazin inverse.

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Available abstract

In this paper, we study the condition for the existence of group inverse, representations of group inverse and Drazin inverse and their computations. A sufficient and necessary condition for the existence of group inverse is given by means of determinantal representation. New representation of group inverse is also presented in terms of original matrix’s maximal nonsingular submatrix. Based on this, we generalize the results to Drazin inverse. Thus we propose a new method to calculate group inverse and Drazin inverse.

Key concepts: Drazin inverse, Mathematics, Invertible matrix, Inverse, Group (periodic table), Inverse element, Representation (politics), Matrix (chemical analysis)

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