Finding a positive definite linear combination of two Hermitian matrices

DOI10.1016/0024-3795(83)90148-9zbMath0516.15021OpenAlexW1979071399MaRDI QIDQ1052434

C. R. Crawford, Yiu Sang Moon

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0024-3795(83)90148-9

zbMATH Keywords

Hermitian matricespositive definite linear combination

Mathematics Subject Classification ID

Related Items (16)

On Local Non-Global Minimizers of Quadratic Optimization Problem with a Single Quadratic Constraint ⋮ Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors ⋮ Hermitian matrix polynomials with real eigenvalues of definite type. I: Classification ⋮ On computing the generalized Crawford number of a matrix ⋮ Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint ⋮ The nearest definite pair for the Hermitian generalized eigenvalue problem ⋮ Matrix pencils: Theory, applications, and numerical methods ⋮ A perturbation bound for definite pencils ⋮ Localization of periodic orbits of polynomial systems by ellipsoidal estimates ⋮ Distance Problems for Hermitian Matrix Pencils with Eigenvalues of Definite Type ⋮ Restoring Definiteness via Shrinking, with an Application to Correlation Matrices with a Fixed Block ⋮ Trace minimization and definiteness of symmetric pencils ⋮ A conjugate gradient-based algorithm for large-scale quadratic programming problem with one quadratic constraint ⋮ Finding a positive definite linear combination of two Hermitian matrices ⋮ Pencils of complex and real symmetric and skew matrices ⋮ Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems

Uses Software

• LINPACK

Cites Work

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• Finding a positive definite linear combination of two Hermitian matrices
• Perturbation bounds for the definite generalized eigenvalue problem
• The $LZ$-Algorithm to Solve the Generalized Eigenvalue Problem
• A Stable Generalized Eigenvalue Problem
• A Theorem on a Mapping from a Sphere to the Circle and the Simultaneous Diagonalization of Two Hermitian Matrices
• Reduction of a band-symmetric generalized eigenvalue problem

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