Eigenvalue inequalities and equalities

DOI10.1016/S0024-3795(97)00031-1zbMath0890.15019MaRDI QIDQ1377499

Roger A. Horn, Noah H. Rhee, Wa-Sin So

Publication date: 26 January 1998

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

zbMATH Keywords

inequalities for eigenvaluesCauchy's interlacing inequalitiesirreducible tridiagonal Hermitian matricesresidual theoremWeyl's inequalities for sums

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (11)

Spectral radius and clique partitions of graphs ⋮ Normal matrices and their principal submatrices of co-order one ⋮ Bounds for the zeros of polynomials from eigenvalues and singular values of some companion matrices ⋮ The eigenvalues range of a class of matrices and some applications in Cauchy-Schwarz inequality and iterative methods ⋮ Total least squares problem with the arbitrary unitarily invariant norms ⋮ A tree whose complement is not eigensharp ⋮ Inequalities and equalities for the Cartesian decomposition of complex matrices ⋮ Cases of equality for certain inequalities involving a \(G\)-doubly stochastic map ⋮ Multi operator-stable random measures and fields ⋮ Refinements of the Hadamard and Cauchy-Schwarz inequalities with two inequalities of the principal angles ⋮ Extension of the total least square problem using general unitarily invariant norms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extended interlacing intervals
• Matrices with some extremal properties
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Certain rank 2K updates act like rank K
• On the eigenvalues and diagonal entries of a Hermitian matrix
• Commutativity and spectra of Hermitian matrices
• Über die Eigenwerte der Summe zweier selbstadjungierter Operatoren
• On the eigenvalues of sums of Hermitian matrices
• Some remarks on the spectra of Hermitian matrices
• Matrix Analysis
• The Monotonicity Theorem, Cauchy's Interlace Theorem, and the Courant- Fischer Theorem
• Refined Interlacing Properties
• The Laguerre Iteration in Solving the Symmetric Tridiagonal Eigenproblem, Revisited
• Principal Submatrices, Geometric Multiplicities, and Structured Eigenvectors
• The Eigenvalues of Complementary Principal Submatrices of a Positive Definite Matrix

This page was built for publication: Eigenvalue inequalities and equalities