The generalized inverse A(2)TS of a matrix over an associative ring

• Autores: Yaoming Yu, Guorong Wang
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 83, Nº 3, 2007, págs. 423-437
• Idioma: inglés
• DOI: 10.1017/s1446788700038015
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• Resumen

  • In this paper we establish the definition of the generalized inverse A(2)TS which is a 2 inverse of a matrix A with prescribed image T and kernel S over an associative ring, and give necessary and sufficient conditions for the existence of the generalized inverse ATS(12) and some explicit expressions for ATS(12) of a matrix A over an associative ring, which reduce to the group inverse or 1 inverses. In addition, we show that for an arbitrary matrix A over an associative ring, the Drazin inverse Ad , the group inverse Ag and the Moore�Penrose inverse A , if they exist, are all the generalized inverse A(2)TS.