Generalized minimax and interlacing theorems

DOI10.1080/03081088408817579zbMath0539.15011OpenAlexW2083748604MaRDI QIDQ3325863

Eduardo Marques de Sá, David H. Carlson

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1080/03081088408817579

zbMATH Keywords

singular valuesinvariant factorsinterlacing inequalitiesproduct of matricessum of matricesmin-max characterizationCourant-Fischer minimax

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (20)

Spectral inequalities for generalized Rayleigh quotients ⋮ Invariants of matrix pairs over discrete valuation rings and Littlewood-Richardson fillings ⋮ On the invariant factors on the matrix \(XAY+B^*\) ⋮ FURTHER GEOMETRIC RESTRICTIONS ON JORDAN STRUCTURE IN MATRIX FACTORIZATION ⋮ Sums and products of matrices with prescribed similarity classes ⋮ Ritz values of normal matrices and Ceva's theorem ⋮ Order bounds for C2-finite sequences ⋮ Invertible bases and root vectors for analytic matrix-valued functions ⋮ Interlacing inequalities. Matrix groups ⋮ ARBITRARINESS OF JORDAN STRUCTURE IN FACTORIZATION: THE GEOMETRIC MULTIPLICITY RESTRICTION AND THE 3 × 3 CASE ⋮ Unified min-max and interlacing theorems for linear operators ⋮ Continuity of submatrices and Ritz sets associated to a point in the numerical range ⋮ Imbedding conditions for normal matrices ⋮ Block imbedding and interlacing results for normal matrices ⋮ Invariant factors of products over elementary divisor domains ⋮ Generalized singular values, interlacing inequalities, and monotonic norms ⋮ Interlacing inequalities for generalized singular values ⋮ Matrix pairs over valuation rings and ℝ-valued Littlewood–Richardson fillings ⋮ Location of Ritz values in the numerical range of normal matrices ⋮ Generalized interlacing inequalities

Cites Work

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• Extreme properties of eigenvalues of a hermitian transformation and singular values of the sum and product of linear transformations
• Eigenvalues of the unitary part of a matrix
• Minimax and interlacing theorems for matrices
• Eigenvalues of sums of Hermitian matrices
• Interlacing inequalities for invariant factors
• Imbedding conditions for \(\lambda\)-matrices
• The eigenvalues and singular values of matrix sums and product. VIII: Displacement of indices
• Principal submatrices. IX: Interlacing inequalities for singular values of submatrices
• Finitely generated modules
• Imbedding Conditions for Hermitian and Normal Matrices
• Equivalence without determinantal divisors^†
• A principal axis transformation for non-hermitian matrices
• Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous Operators

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