Finite criteria for conditional definiteness of quadratic forms

DOI10.1016/0024-3795(81)90286-XzbMath0464.15012MaRDI QIDQ1153967

S. H. Smith

Publication date: 1981

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

zbMATH Keywords

symmetric matricescopositive matricesconditionally positive semidefinite matrices

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Quadratic and bilinear forms, inner products (15A63)

Related Items

Testing the definiteness of matrices on polyhedral cones ⋮ Remarks on the recursive structure of copositivity ⋮ Think co(mpletely)positive! Matrix properties, examples and a clustered bibliography on copositive optimization ⋮ An algorithm for determining copositive matrices ⋮ On a decomposition of conditionally positive-semidefinite matrices ⋮ Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method ⋮ Algebra -- 9. Translated from the Russian ⋮ Optimization of a nonlinear Hermitian matrix expression with application ⋮ Algorithmic copositivity detection by simplicial partition ⋮ Bitopological spaces ⋮ Copositive realxation for genera quadratic programming ⋮ The 123 theorem of probability theory and copositive matrices ⋮ Copositive Lyapunov functions for switched systems over cones ⋮ Investigations in topology. 9. Work collection ⋮ Conditionally definite matrices ⋮ Bitopologies on products and ratios ⋮ On copositive matrices ⋮ ON CONDITIONALLY DEFINITE QUADRATIC FORMS ⋮ A finite algorithm for solving general quadratic problems

Cites Work

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• Linear inequalities and quadratic forms
• Necessary and sufficient conditions for a quadratic form to be positive whenever a set of homogeneous linear constraints is satisfied
• Manifestations of the Schur complement
• Two remarks on copositive matrices
• On classes of copositive matrices
• On values and strategies for infinite-time linear quadratic games
• A finite procedure for determining if a quadratic form is bounded below on a closed polyhedral convex set
• An alternative method for a global analysis of quadratic programs in a finite number of steps
• Shadows of finite sets
• Quadratic Forms with Linear Constraints

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