A generalization of Sylvester's identity on determinants and some applications
type: Item
instance of: scholarly article
title: A generalization of Sylvester's identity on determinants and some applications
zbMATH Open document ID: 0576.15005
DOI: 10.1016/0024-3795(85)90134-X
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 3920680
zbMATH Keywords: inequalities for determinants
zbMATH Keywords: Sylvester's identity on determinants
zbMATH Keywords: elimination method
zbMATH Keywords: Laplacian expansion
author: Günter W. Mühlbach
author: M. Gasca
reviewed by: Nikolai I. Osetinski
MaRDI profile type: Publication
cites work: Q3329899
cites work: Determinantal identities: Gauss, Schur, Cauchy, Sylvester, Kronecker, Jacobi, Binet, Laplace, Muir, and Cayley
cites work: Q3849175
cites work: Q3961261
cites work: Elimination techniques and interpolation
cites work: Q5624248
cites work: Two composition methods for solving certain systems of linear equations
cites work: Q3922071
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description: scientific article; zbMATH DE number 3920680