Galba, E. F., et al. “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, https://umj.imath.kiev.ua/index.php/umj/article/view/1992.