Procrustes problems and associated approximation problems for matrices with \(k\)-involutory symmetries

DOI10.1016/j.laa.2010.09.044zbMath1213.15014OpenAlexW2062289683MaRDI QIDQ616417

Xi-Yan Hu, Jiao-Fen Li

Publication date: 7 January 2011

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

Full work available at URL: https://doi.org/10.1016/j.laa.2010.09.044

zbMATH Keywords

eigenvaluesminimal polynomialinvolutory matrixapproximation problemProcrustes problems\((R, S, \alpha, \mu)\)-symmetric matrix\((R, S, \mu)\)-symmetric matrix

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Inverse problems in linear algebra (15A29) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (4)

Structured least-squares problems and inverse eigenvalue problems for \((P,Q)\)-reflexive matrices ⋮ The solutions to linear matrix equations \(AX=B\), \(YA=D\) with \(k\)-involutory symmetries ⋮ Procrustes problems and inverse eigenproblems for multilevel block α -circulants ⋮ Inverse problems for unilevel block α‐circulants

Cites Work

• The solvability conditions for the inverse eigenvalue problems of reflexive matrices
• Procrustes problems for (\(P,Q,\eta \))-reflexive matrices
• Characterization and properties of matrices with \(k\)-involutory symmetries
• Characterization and properties of matrices with \(k\)-involutory symmetries. II
• The reflexive and anti-reflexive solutions of the matrix equation \(AX=B\).
• Inverse eigenproblems and associated approximation problems for matrices with generalized symmetry or skew symmetry.
• Least-square solutions for inverse problems of centrosymmetric matrices
• The solvability conditions for the inverse eigenvalue problems of centro-symmetric matrices
• Minimization problems for \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices
• Pseudo-centrosymmetric matrices, with applications to counting perfect matchings
• Centrosymmetric (Cross-Symmetric) Matrices, Their Basic Properties, Eigenvalues, and Eigenvectors
• Circulative Matrices of Degree $\theta $
• Generalized Reflexive Matrices: Special Properties and Applications
• Mirrorsymmetric Matrices, Their Basic Properties, and an Application on Odd/Even-Mode Decomposition of Symmetric Multiconductor Transmission Lines
• Characterization and Properties of (R,S)-Symmetric, (R,S)-Skew Symmetric, and (R,S)-Conjugate Matrices

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