H-Unitary and Lorentz Matrices: A Review

DOI10.1137/S0895479803421896zbMath1063.15021OpenAlexW2022578933MaRDI QIDQ4650977

Chi-Kwong Li, Yik-Hoi Au-Yeung, Leiba Rodman

Publication date: 21 February 2005

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0895479803421896

zbMATH Keywords

Hermitian matricesindefinite inner productsurvey paperunitary matricesLorentz matricesCD-decompositiondiagonalizable \(H\)-unitary matricespositive definite \(J\)-unitary matrices

Mathematics Subject Classification ID

Factorization of matrices (15A23) Hermitian, skew-Hermitian, and related matrices (15B57) Quadratic and bilinear forms, inner products (15A63) Canonical forms, reductions, classification (15A21) Research exposition (monographs, survey articles) pertaining to linear algebra (15-02)

Related Items (8)

Isometric and selfadjoint operators on a vector space with nondegenerate diagonalizable form ⋮ Normal forms for symplectic matrices ⋮ Linear maps transforming \(H\)-unitary matrices. ⋮ Unitary groups of nondegenerate Hermitian forms and the homotopy groups of pseudospheres ⋮ Classification of linear operators satisfying \((Au,v)=(u,a^rv)\) or \((Au,a^rv)=(u,v)\) on a vector space with indefinite scalar product ⋮ Canonical matrices of isometric operators on indefinite inner product spaces ⋮ Basic classes of matrices with respect to quaternionic indefinite inner product spaces ⋮ Similarity vs unitary similarity and perturbation analysis of sign characteristics: complex and real indefinite inner products

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