Optimization Online


A revisit to a reverse-order law for generalized inverses of a matrix product and its variations

Yongge Tian (yongge.tian***at***gmail.com)

Abstract: This paper approaches a fundamental reverse-order law $(AB)^{(1)} = B^{\dag}A^{\dag}$ in the theory of generalized inverse, where $A$ and $B$ are $m \times n$ and $n \times p$ complex matrices, respectively, $(AB)^{(1)}$ is $\{1\}$-inverse of $AB$, $A^{\dag}$ and $B^{\dag}$ are the Moore--Penrose inverses of $A$ and $B$, respectively. We will collect and derive many known and novel equivalent statements for the reverse-order law and its variations to hold by using the methodology of ranks and ranges of matrices.

Keywords: matrix product, Moore--Penrose inverse, reverse-order law, rank, range

Category 1: Global Optimization (Theory )


Download: [PDF]

Entry Submitted: 08/24/2017
Entry Accepted: 08/24/2017
Entry Last Modified: 09/11/2017

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society