Regular matrices and their generalized inverses over the max algebra
Kyung-Tae Kang, Seok-Zun Song · Linear and Multilinear Algebra · 2014
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.