Necessary and Sufficient Conditions for the Existence of Weighted Singular-Valued Decompositions of Matrices with Singular Weights
AbstractA 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.
How to Cite
Galba, E. F., V. S. Deineka, and I. V. Sergienko. “Necessary and Sufficient Conditions for the Existence of Weighted Singular-Valued Decompositions of Matrices With Singular Weights”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 3, Mar. 2015, pp. 406–426, http://umj.imath.kiev.ua/index.php/umj/article/view/1992.