A generalization of Sylvester's identity on determinants and some applications
The authors propose a method of deriving a generalization of Sylvester's identity on determinants [cf. the second author, \textit{A. Lopez-Carmona} and \textit{V. Ramirez}, Multivariate approximation theory II, Proc. Conf., Oberwolfach 1982, ISNM 61, 171-184 (1982; Zbl 0496.41002)] which is based upon the elimination method [see, for example, the first author, Extrapolation algorithms as elimination techniques with applications to systems of linear equations, Report 152, Inst. Mathematik Univ. Hannover (1982)] and on Laplacian expansion. They apply this identity for generalization of some inequalities between determinants of a special type considered by \textit{S. Karlin} [Total positivity, Vol. I (1968; Zbl 0219.47030)].
scientific article; zbMATH DE number 3920680
scientific article