New proofs and extensions of Sylvester’s and Johnson’s inertia theorems to non-Hermitian matrices

DOI10.1090/S0002-9939-2011-11232-2zbMath1245.15015OpenAlexW2051845165MaRDI QIDQ3103254

Man Kam Kwong, Anton Zettl

Publication date: 7 December 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-11232-2

zbMATH Keywords

Hermitian matrixpositive definite matrixmatrix eigenvalueseigenvalue curvespositive and negative eigenvaluesSylvester inertia theorem

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Determinants, permanents, traces, other special matrix functions (15A15) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Cites Work

• Unnamed Item
• On Ostrowski's generalization of Sylvester's law of inertia
• A quantitative formulation of Sylvester's law of inertia. III
• The inertia of a product of two hermitian matrices
• Matrix Analysis
• Left-definite Sturm-Liouville problems