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Matrix equalities equivalent to the reverse order law $(AB)^{\dag} = B^{\dag}A^{\dag}$
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: Received: 23 November 2020 / Approved: 23 November 2020 / Online: 23 November 2020 (14:20:44 CET)
How to cite: Tian, Y. Matrix equalities equivalent to the reverse order law $(AB)^{\dag} = B^{\dag}A^{\dag}$. Preprints 2020, 2020110587 Tian, Y. Matrix equalities equivalent to the reverse order law $(AB)^{\dag} = B^{\dag}A^{\dag}$. Preprints 2020, 2020110587
Abstract
This note shows that the well-known reverse order law $(AB)^{\dag} = B^{\dag}A^{\dag}$ for the Moore--Penrose inverse of matrix product is equivalent to many other equalities for that are composed of multiple products $(AB)^{\dag}$ and $B^{\dag}A^{\dag}$ by means of the definition of the Moore--Penrose inverse and orthogonal projector theory.
Keywords
matrix product; Moore-Penrose inverse; reverse order law; orthogonal projector
Subject
Computer Science and Mathematics, Algebra and Number Theory
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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