Quaternion involutions and anti-involutions

DOI10.1016/j.camwa.2006.10.029zbMath1131.11072arXivmath/0506034OpenAlexW2040575700WikidataQ56213064 ScholiaQ56213064MaRDI QIDQ2469923

Stephen J. Sangwine, Todd A. Ell

Publication date: 11 February 2008

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506034

zbMATH Keywords

involutionquaternionanti-involution

Mathematics Subject Classification ID

Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (20)

Lie algebra of unit tangent bundle ⋮ Involutions in dual split-quaternions ⋮ Involutions of complexified quaternions and split quaternions ⋮ Unnamed Item ⋮ Least squares η-bi-Hermitian problems of the quaternion matrix equation (AXB,CXD) = (E,F) ⋮ Augmented second-order statistics of quaternion random signals ⋮ A broad class of discrete-time hypercomplex-valued Hopfield neural networks ⋮ Classification of involutive automorphisms and anti-automorphisms of the Lie algebra of quaternions ⋮ Functional equations for vector products and quaternions ⋮ Matrix LSQR algorithm for structured solutions to quaternionic least squares problem ⋮ Fundamental representations and algebraic properties of biquaternions or complexified quaternions ⋮ Dual quaternion involutions and anti-involutions ⋮ On the unitary diagonalisation of a special class of quaternion matrices ⋮ Some results for the two-sided quaternionic Gabor Fourier transform and quaternionic Gabor frame operator ⋮ Consimilarity of quaternions and coneigenvalues of quaternion matrices ⋮ Characterizations of automorphic and anti-automorphic involutions of the quaternions ⋮ A new eigenspace characterization of split-quaternion involutions ⋮ L-structured quaternion matrices and quaternion linear matrix equations ⋮ Semi-Euclidean quasi-elliptic planar motion ⋮ Least-squares problem for the quaternion matrix equationAXB+CYD=Eover different constrained matrices

Cites Work

• On Rings with Involution
• Hamilton and Jacobi Meet Again: Quaternions and the Eigenvalue Problem
• Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case
• Quaternions and Reflections
• Hamilton and Jacobi come full circle: Jacobi algorithms for structured Hamiltonian eigenproblems
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