Several consequences of an inertia theorem

DOI10.1016/0024-3795(90)90020-DzbMath0712.15021OpenAlexW2038934782MaRDI QIDQ923673

Jerome Dancis

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0024-3795(90)90020-d

zbMATH Keywords

quadratic programmingalgebraic Riccati equationHamiltonian matricespositive semidefinite Hermitian matricesinertia of a matrixpositive and negative eigenvalues

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items

A restricted signature normal form for Hermitian matrices, quasi-spectral decompositions, and applications ⋮ Solutions of a constrained Hermitian matrix-valued function optimization problem with applications ⋮ Quadratic properties of least-squares solutions of linear matrix equations with statistical applications ⋮ Maximization and minimization of the rank and inertia of the Hermitian matrix expression \(A-BX-(BX)^{*}\) with applications ⋮ Rank/inertia approaches to weighted least-squares solutions of linear matrix equations ⋮ Ranks and inertias of Hermitian block Toeplitz matrices ⋮ Matrix rank/inertia formulas for least-squares solutions with statistical applications

Cites Work

• Unnamed Item
• Unnamed Item
• An interlacing theorem for eigenvalues of self-adjoint operators
• On the inertias of symmetric matrices and bounded self-adjoint operators
• The possible inertias for a Hermitian matrix and its principal submatrices
• Determination of the inertia of a partitioned Hermitian matrix
• On the interia of some classes of partitioned matrices
• Matrix-theoretic criteria for the quasi-convexity and pseudo-convexity of quadratic functions
• The Numerical Solution of Equality-Constrained Quadratic Programming Problems
• Subdefinite Matrices and Quadratic Forms
• Quadratic Programming with a Quasiconvex Objective Function
• The Stabilizing Solution of the Algebraic Riccati Equation