Matrix splittings and generalized inverses
Copyright policy )Matrix splittings and generalized inverses
Summary: We introduce a splitting of the class of square singular complex matrices induced by its inner inverses in two ways: using the Jordan normal form, and using the concept of condiagonalizability. Then, we use the introduced splitting to prove a special case of Harte's theorem [\textit{R. Harte}, Proc. Am. Math. Soc. 99, 328--330 (1987; Zbl 0617.46052)] for complex matrices.
condiagonalizability, generalized inverses, Canonical forms, reductions, classification, matrix splitting, Jordan normal form, Theory of matrix inversion and generalized inverses, Harte's theorem
condiagonalizability, generalized inverses, Canonical forms, reductions, classification, matrix splitting, Jordan normal form, Theory of matrix inversion and generalized inverses, Harte's theorem
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