The \(\phi_S\) polar decomposition

DOI10.1016/j.laa.2012.07.026zbMath1262.15011OpenAlexW1983390144MaRDI QIDQ1932634

Daryl Q. Granario, Dennis I. Merino, Agnes T. Paras

Publication date: 21 January 2013

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.07.026

zbMATH Keywords

symmetric matrixpolar decompositionskew symmetric matrixorthogonal matrixJordan canonical forms

Mathematics Subject Classification ID

Factorization of matrices (15A23) Hermitian, skew-Hermitian, and related matrices (15B57) Canonical forms, reductions, classification (15A21) Polar geometry, symplectic spaces, orthogonal spaces (51A50) Orthogonal matrices (15B10)

Related Items (7)

On the Lie algebra associated to \(S\)-unitary matrices ⋮ The phiS polar decomposition when the cosquare of S is nonderogatory ⋮ The \(\phi_S\) polar decomposition when the cosquare of \(S\) is normal ⋮ 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 \(-1\notin \sigma(S^{-T}S)\) ⋮ On the diagonalizability of a matrix by a symplectic equivalence, similarity or congruence transformation ⋮ \(S\) orthogonal matrices and \(S\) symmetries

Cites Work

• Unnamed Item
• The \(\phi _S\) polar decomposition of matrices
• \(\phi_S\)-orthogonal matrices
• Contragredient equivalence: A canonical form and some applications
• The Jordan canonical forms of complex orthogonal and skew-symmetric matrices
• Algebraic Polar Decomposition
• Matrix Analysis

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