Distributions of eigenvalues and inertias of some block Hermitian matrices consisting of orthogonal projectors

DOI10.1080/03081087.2011.631922zbMath1261.15013OpenAlexW2120707918MaRDI QIDQ5200336

Ying Li, Yongge Tian

Publication date: 5 November 2012

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

Full work available at URL: https://doi.org/10.1080/03081087.2011.631922

zbMATH Keywords

signaturerankinertiamatrix inequalityHermitian matrixorthogonal projectorblock matrixpartial orderingdistribution of eigenvalues

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) Hermitian, skew-Hermitian, and related matrices (15B57) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

Some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix equation restrictions ⋮ On relationships between two linear subspaces and two orthogonal projectors

Cites Work

• Equalities for orthogonal projectors and their operations
• Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors
• A gentle guide to the basics of two projections theory
• Equalities and inequalities for inertias of Hermitian matrices with applications
• On linear combinations of two idempotent matrices over an arbitrary field
• Column space equalities for orthogonal projectors
• On the generalized derivation induced by two projections
• The structure of a real linear combination of two projections
• On the product of orthogonal projectors
• The index of a pair of projections
• \(C^*\)-algebras generated by orthogonal projections and their applications
• Applications of CS decomposition in linear combinations of two orthogonal projectors
• Rank equalities for idempotent matrices with applications.
• Determination of the inertia of a partitioned Hermitian matrix
• On the interia of some classes of partitioned matrices
• On the spectra of sums of orthogonal projections with applications to parallel computing
• Subspaces, angles and pairs of orthogonal projections
• On the spectrum of linear combinations of two projections inC*-algebras
• Products of orthogonal projections
• On the algebra generated by two projections
• The $C^*$-algebra generated by two projections.
• Rank equalities for idempotent and involutory matrices