The computation and perturbation analysis for weighted group inverse of rectangular matrices (Q1034946)

The weighted group inverse \(A^{\#}_W\) of a matrix \(A \in \mathbb{C}^{m\times n}\) with respect to a matrix \(W \in \mathbb{C}^{n\times m}\) was defined by \textit{J. Cen} [Math. Numer. Sin. 29, No.~1, 39--48 (2007; Zbl 1121.15303)] as the solution \(X\in \mathbb{C}^{n \times m}\) of the matrix equations \(AWXWA= A, XWAWX = X, AWX=XWA\). The present authors study algebraic perturbations and analytical perturbations of the weighted group inverse \(A^{\#}_W\), and give a new representation based on Gauss elimination. They use this representation to compute the weighted group inverse.