Working Paper Article Version 1 This version is not peer-reviewed

Matrix equalities equivalent to the reverse order law $(AB)^{\dag} = B^{\dag}A^{\dag}$

Version 1 : 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.

Subject Areas

matrix product; Moore-Penrose inverse; reverse order law; orthogonal projector

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