- A revisit to a reverse-order law for generalized inverses of a matrix product and its variations Yongge Tian (yongge.tiangmail.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 ) Citation: Download: [PDF]Entry Submitted: 08/24/2017Entry Accepted: 08/24/2017Entry Last Modified: 09/11/2017Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.