@article{Galba_Deineka_Sergienko_2015, title={Necessary and Sufficient Conditions for the Existence of Weighted Singular-Valued Decompositions of Matrices with Singular Weights}, volume={67}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/1992}, abstractNote={A weighted singular-valued decomposition of matrices with singular weights is obtained by using orthogonal matrices. The necessary and sufficient conditions for the existence of the constructed weighted singular-valued decomposition are established. The indicated singular-valued decomposition of matrices is used to obtain a decomposition of their weighted pseudoinverse matrices and decompose them into matrix power series and products. The applications of these decompositions are discussed.}, number={3}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Galba, E. F. and Deineka, V. S. and Sergienko, I. V.}, year={2015}, month={Mar.}, pages={406–426} }