Norm estimations for the Moore-Penrose inverse of multiplicative perturbations of matrices (Q5962569)

By a multiplicative perturbation of a matrix \(A \in \mathbb{C}^{m\times n}\) we mean a matrix \(B=D_1^*AD_2 \in \mathbb{C}^{n\times m}\), where \(D_1\) and \(D_2\) are nonsingular square matrices. Without using the singular value decomposition (SVD), the authors derive new upper bounds for the Frobenius norm and the spectral norm of \(B^\dagger-A^\dagger\), where \(^\dagger\) denotes the Moore-Penrose inverse action. They also provide improvements of some results of \textit{L. Meng} and \textit{B. Zheng} [Linear Multilinear Algebra 63, No. 5, 1037--1048 (2015; Zbl 1312.15007)] for these norms.