Singular values, doubly stochastic matrices, and applications

DOI10.1016/0024-3795(95)00111-4zbMath0828.15007OpenAlexW2092204459WikidataQ126789349 ScholiaQ126789349MaRDI QIDQ1893086

Shmuel Friedland, Ludwig Elsner

Publication date: 11 January 1996

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

Full work available at URL: https://doi.org/10.1016/0024-3795(95)00111-4

zbMATH Keywords

graphcycleHadamard productnonnegative matricessingular valuesdoubly stochastic matricesperturbation of eigenvaluesHoffman-Wielandt inequality

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Stochastic matrices (15B51)

Related Items (20)

Perturbation bounds for eigenvalues of diagonalizable matrices and singular values ⋮ Multiplicative relative perturbation bounds of eigenvalues for diagonalizable matrices ⋮ New upper bounds for the spectral variation of a general matrix ⋮ On interval estimates of perturbations of generalized eigenvalues for diagonalizable pairs ⋮ On symplectic eigenvalues of positive definite matrices ⋮ On perturbation bounds of generalized eigenvalues for diagonalizable pairs ⋮ Spectral variation bounds for diagonalisable matrices ⋮ Relative perturbation theory. III: More bounds on eigenvalue variation ⋮ Relative perturbation theory for matrix eigenproblems in free vibration analysis ⋮ Hoffman-Wielandt type inequality for block companion matrices of certain matrix polynomials ⋮ On generalizing trace minimization principles. II ⋮ Relative perturbation theory for hyperbolic eigenvalue problem ⋮ Revisiting IRKA: connections with pole placement and backward stability ⋮ Relative perturbation bounds for eigenpairs of diagonalizable matrices ⋮ Bounds for relative distances of eigenvalues in free vibration analysis ⋮ Efficient numerical algorithms for constructing orthogonal generalized doubly stochastic matrices ⋮ A note on the Hoffman-Wielandt theorem for generalized eigenvalue problems ⋮ Spectral variations and Hadamard products: Some problems ⋮ A note on unifying absolute and relative perturbation bounds ⋮ Relative perturbation theory for hyperbolic singular value problem

Cites Work

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• The complexity of computing the permanent
• Every 7-regular digraph contains an even cycle
• Proof of the van der Waerden conjecture regarding the permanent of a doubly stochastic matrix
• A proof of Fulkerson's characterization of permutation matrices
• A note on the Hoffman-Wielandt theorem
• Additive decomposition of nonnegative matrices with applications to permanents and scalingt
• A proof of a generalized van der Waerden conjecture on permanents
• The Even Cycle Problem for Directed Graphs
• On perturbations of matrix pencils with real spectra, a revisit
• The Maximum Number of Disjoint Permutations Contained in a Matrix of Zeros and Ones

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