A generalization of Sylvester's identity on determinants and some applications

DOI10.1016/0024-3795(85)90134-XzbMath0576.15005MaRDI QIDQ1065104

Mariano Gasca, Günter W. Mühlbach

Publication date: 1985

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

elimination methodinequalities for determinantsLaplacian expansionSylvester's identity on determinants

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Miscellaneous inequalities involving matrices (15A45)

Related Items

Generalized Schur-complements and a test for total positivity, Some Schur complement identities and applications to matrix extrapolation methods, Linear extrapolation by rational functions, exponentials and logarithmic functions, Algebraic properties of Manin matrices. I, Matrix extrapolation algorithms, Other manifestations of the Schur complement, The work of Mariano Gasca, On some determinantal identities formation laws, On extending determinantal identities, Can Sylvester's determinantal identity, equivalently Muir's law of extensible minors be generalized?, Convergence properties of some block Krylov subspace methods for multiple linear systems, Computation of rational interpolants with prescribed poles, ECT-B-splines defined by generalized divided differences, Elimination techniques: From extrapolation to totally positive matrices and CAGD, A generalization of Mühlbach's extension principle for determinantal identities, A general determinantal identity of Sylvester type and some applications

Cites Work

• Determinantal identities: Gauss, Schur, Cauchy, Sylvester, Kronecker, Jacobi, Binet, Laplace, Muir, and Cayley
• Two composition methods for solving certain systems of linear equations
• Elimination techniques and interpolation
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