The reverse order law for the weighted least square g-inverse of multiple matrix products

Abstract

By using the ranks of the generalized Schur complement, the equivalent conditions for reverse order laws of the $ \{1, 3M\}- $ and the $ \{1, 4N\}- $ inverses of the multiple product of matrices are derived.

Keywords

• reverse order law
• weighted least square $ g $-inverse
• matrix product
• generalized schur complement
• maximal and minimal ranks