Takane, Yoshio; Tian, Yongge; Yanai, Haruo On reverse-order laws for least-squares g-inverses and minimum norm g-inverses of a matrix product. (English) Zbl 1125.15006 Aequationes Math. 73, No. 1-2, 56-70 (2007). The reverse order law is analyzed for some kinds of generalized inverses: \((1,3)\) and \((1,4)\) generalized inverses and the Moore-Penrose inverse. For example, relations indicating when \(B^{(1,i)}A^{(1,i)} \in (AB)^{(1,i)}\) are studied for \(i=3,4\) and when the equality holds for the Moore-Penrose inverse. Reviewer: Nestor Thome (Valencia) Cited in 9 Documents MSC: 15A09 Theory of matrix inversion and generalized inverses 15A03 Vector spaces, linear dependence, rank, lineability Keywords:least-squares g-inverse; matrix product; matrix rank method; minimum norm g-inverse; Moore-Penrose inverse; reverse-order law PDFBibTeX XMLCite \textit{Y. Takane} et al., Aequationes Math. 73, No. 1--2, 56--70 (2007; Zbl 1125.15006) Full Text: DOI