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Further Results on a Matrix Equality and Matrix Set Inclusions for Generalized Inverses of Matrix Products
Version 1
: Received: 5 June 2020 / Approved: 5 June 2020 / Online: 5 June 2020 (14:41:12 CEST)
How to cite: Tian, Y. Further Results on a Matrix Equality and Matrix Set Inclusions for Generalized Inverses of Matrix Products. Preprints 2020, 2020060057 Tian, Y. Further Results on a Matrix Equality and Matrix Set Inclusions for Generalized Inverses of Matrix Products. Preprints 2020, 2020060057
Abstract
This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.
Keywords
generalized inverse; matrix product; matrix equality; reverse order law; set inclusion; rank equality
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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