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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 3, pp. 406–426, March, 2015.
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Sergienko, I.V., Galba, E.F. & Deineka, V.S. Necessary and Sufficient Conditions for the Existence of Weighted Singular-Valued Decompositions of Matrices with Singular Weights. Ukr Math J 67, 464–486 (2015). https://doi.org/10.1007/s11253-015-1093-1
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DOI: https://doi.org/10.1007/s11253-015-1093-1