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Regular matrices and their generalized inverses over the max algebra

Author： Kang Kyung-Tae   Song Seok-Zun  

Publisher： Taylor & Francis Ltd

E-ISSN： 1563-5139|63|8|1649-1663

ISSN： 0308-1087

Source： Linear and Multilinear Algebra, Vol.63, Iss.8, 2015-08, pp. : 1649-1663

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Abstract

For an matrix over the max algebra , a generalized inverse of is an matrix over satisfying . In this paper, we determine the general form of matrices having generalized inverses. Also, we define a space decomposition of a matrix, and prove that a matrix has a generalized inverse if and only if it has a space decomposition. Using this decomposition, we characterize reflexive -inverses of matrices. Furthermore, we establish necessary and sufficient conditions for a matrix to possess various types of -inverses including Moore–Penrose inverse.

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