Submitted:
23 November 2020
Posted:
23 November 2020
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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
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