Wielandt and Ky-Fan theorem for matrix pairs.

DOI10.1016/S0024-3795(02)00733-4zbMath1035.15021MaRDI QIDQ1399921

Krešimir Veselić, Ivica Nakić

Publication date: 30 July 2003

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

zbMATH Keywords

Cauchy inequalitypositive definite matrixmatrix pencilsquadratic pencilseigenvalue perturbation boundsWielandt theoremKy-Fan theorems

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Matrix pencils (15A22)

Related Items

Extensions of Wielandt’s min–max principles for positive semi-definite pencils, Optimization on the symplectic Stiefel manifold: SR decomposition-based retraction and applications, Linear pencils and quadratic programming problems with a quadratic constraint, Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem, Computing Symplectic Eigenpairs of Symmetric Positive-Definite Matrices via Trace Minimization and Riemannian Optimization

Cites Work

• Extreme properties of eigenvalues of a hermitian transformation and singular values of the sum and product of linear transformations
• Matrices and indefinite scalar products
• The Lidskii-Mirsky-Wielandt theorem -- additive and multiplicative versions
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• Generalized eigenvalues of a definite Hermitian matrix pair
• Variational principles for real eigenvalues of self-adjoint operator pencils
• Variational principles for indefinite eigenvalue problems
• Trace minimization and definiteness of symmetric pencils
• A note on Stewart's theorem for definite matrix pairs
• A variational principle for eigenvalues of pencils of Hermitian matrices
• A Trace Minimization Algorithm for the Generalized Eigenvalue Problem
• A Variational Principle in Krein Space
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