Necessary and Sufficient Conditions for the Existence of Weighted Singular-Valued Decompositions of Matrices with Singular Weights

  • E. F. Galba
  • V. S. Deineka
  • I. V. Sergienko

Abstract

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.
Published
25.03.2015
How to Cite
GalbaE. F., DeinekaV. S., and SergienkoI. V. “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.
Section
Research articles