Some topics on weighted Moore-Penrose inverse, weighted least squares and weighted regularized Tikhonov problems (Q1888517)

\textit{D. J. Higham} [Linear Algebra Appl. 214, 193--213 (1995; Zbl 0816.15004)] gave the definition and formulae of the condition number under the spectral and Frobenius matrix norms in \(\mathbb{R}^{m\times n}\). The present author extends these results to two weighted matrix norms in \(\mathbb{C}^{m\times n}\). Moreover, the nearness to rank deficiency is considered. The regularized weighted Tikhonov problem is studied based on a generalized weighted singular value decomposition.