Necessary and Sufficient Conditions for the Existence of Weighted Singular-Valued Decompositions of Matrices with Singular Weights
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.
English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 3, pp 464-486.
Citation Example: Deineka V. S., Galba E. F., Sergienko I. V. Necessary and Sufficient Conditions for the Existence of Weighted Singular-Valued Decompositions of Matrices with Singular Weights // Ukr. Mat. Zh. - 2015. - 67, № 3. - pp. 406–426.