Canonical forms for unitary congruence and *congruence

DOI10.1080/03081080802079309zbMath1183.15010arXiv0710.1530OpenAlexW2005397551MaRDI QIDQ3648445

Vladimir V. Sergeichuk, Roger A. Horn

Publication date: 26 November 2009

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

Full work available at URL: https://arxiv.org/abs/0710.1530

zbMATH Keywords

canonical formsunitary matricesunitary congruence\(^*\)congruence

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Canonical forms, reductions, classification (15A21)

Related Items (18)

Checking the congruence between accretive matrices ⋮ Tensor space representations of Temperley–Lieb algebra and generalized permutation matrices ⋮ The orthogonality relation classifies finite-dimensional formally real simple Jordan algebras ⋮ Rationally verifiable necessary conditions for Hermitian congruence of complex matrices ⋮ Unnamed Item ⋮ On the solvability of a certain class of quadratic matrix equations ⋮ The \(\phi_S\) polar decomposition when the cosquare of \(S\) is normal ⋮ THE GEOMETRIC PICTURE OF GENERALIZED-CP AND HIGGS-FAMILY TRANSFORMATIONS IN THE TWO-HIGGS-DOUBLET MODEL ⋮ Canonical matrices of bilinear and sesquilinear forms ⋮ Orthogonal similarity of a real matrix and its transpose ⋮ On the field of values of oblique projections ⋮ The \(\psi_{S}\) polar decomposition when the cosquare of \(S\) is normal ⋮ The sum of two \(\phi_{S}\) orthogonal matrices when \(S^{-T}S\) is normal and \(-1\notin \sigma(S^{-T}S)\) ⋮ Square roots of Hermitian matrices and a rational algorithm for checking their congruence ⋮ Classification of squared normal operators on unitary and Euclidean spaces ⋮ OPUC, CMV matrices and perturbations of measures supported on the unit circle ⋮ On the singular value decomposition of (skew-)involutory and (skew-)coninvolutory matrices ⋮ \(S\) orthogonal matrices and \(S\) symmetries

Cites Work

• A real-coninvolutory analog of the polar decomposition
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• Some observations on the Youla form and conjugate-normal matrices
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• Unitary and Euclidean representations of a quiver
• Unitary similarity of matrices with quadratic minimal polynomials
• Complexity of matrix problems
• Congruences of a square matrix and its transpose
• Canonical forms for complex matrix congruence and \(^{*}\)-congruence
• A regularization algorithm for matrices of bilinear and sesquilinear forms
• Normal Form of Antiunitary Operators
• Matrix Analysis
• Canonical Form for Matrices Under Unitary Congruence Transformations. I: Conjugate-normal Matrices
• On the conjugacy classes in the unitary, symplectic and orthogonal groups
• On Unitary Equivalence
• On the Theory of Automorphic Functions of a Matrix Variable I-Geometrical Basis
• A generalization of Sylvester's law of inertia

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