Characterization and properties of matrices with \(k\)-involutory symmetries. II

DOI10.1016/j.laa.2009.12.015zbMath1205.15014OpenAlexW2013960781MaRDI QIDQ967496

William F. Trench

Publication date: 29 April 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.12.015

zbMATH Keywords

eigenvalue problemdiscrete Fourier transformMoore-Penrose inversecirculantblock circulantcocirculant

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Basic linear algebra (15A99)

Related Items (12)

Algorithms for solving the inverse problem associated with \(KAK=A^{s+1}\) ⋮ Similar powers of a matrix ⋮ The solutions to linear matrix equations \(AX=B\), \(YA=D\) with \(k\)-involutory symmetries ⋮ Matrices \(A\) such that \(RA = A^{s+1}R\) when \(R^k = I\) ⋮ Procrustes problems and associated approximation problems for matrices with \(k\)-involutory symmetries ⋮ On a matrix group constructed from an \(\{ R,s+1,k \}\)-potent matrix ⋮ Characterization and properties of \((R,S_\sigma)\)-commutative matrices ⋮ Inverse problems for unilevel block α‐circulants ⋮ Matrices \(A\) such that \(A^{s+1}R\) = \(RA^\ast\) with \(R^k = I\) ⋮ Characterization and properties of \((P_\sigma, Q)\) symmetric and co-symmetric matrices ⋮ An inverse eigenproblem for generalized reflexive matrices with normal $k+1$-potencies ⋮ Generalized centro-invertible matrices with applications

Cites Work

• Properties of multilevel block \(\alpha \)-circulants
• Characterization and properties of matrices with \(k\)-involutory symmetries
• Properties of unilevel block circulants
• Matrices with multiple symmetry properties: applications of centro-Hermitian and per-Hermitian matrices
• Characterization and properties of matrices with generalized symmetry or skew symmetry.
• Generalized inverses. Theory and applications.
• Eigenvectors of certain matrices
• A Spectral Characterization of Generalized Real Symmetric Centrosymmetric and Generalized Real Symmetric Skew-Centrosymmetric Matrices
• Centrosymmetric (Cross-Symmetric) Matrices, Their Basic Properties, Eigenvalues, and Eigenvectors
• A Matrix Decomposition Method for Orthotropic Elasticity Problems
• Roots and Canonical Forms for Circulant Matrices
• Circulative Matrices of Degree $\theta $
• Cyclic Transformations of Polygons and the Generalized Inverse
• Classroom Note:Centrosymmetric Matrices
• Spectral Characterizations for Hermitian Centrosymmetric K-Matrices and Hermitian Skew-Centrosymmetric K-Matrices
• Mirrorsymmetric Matrices, Their Basic Properties, and an Application on Odd/Even-Mode Decomposition of Symmetric Multiconductor Transmission Lines
• The Inverse of a Centrosymmetric Matrix
• The Pseudoinverse of an r-Circulant Matrix
• Solution of Equations Involving Centrosymmetric Matrices

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