Hamilton and Jacobi Meet Again: Quaternions and the Eigenvalue Problem

DOI10.1137/S0895479893257055zbMath0824.65021MaRDI QIDQ4835404

Niloufer Mackey

Publication date: 22 October 1995

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

zbMATH Keywords

block diagonalizationnumerical algorithmsJacobi algorithm\(4 \times 4\)-symmetric matrixHamilton's algebra of quaternions

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Multilinear algebra, tensor calculus (15A69) Canonical forms, reductions, classification (15A21) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (10)

An elementary, first principles approach to the indefinite spin groups ⋮ An algorithm to compute the polar decomposition of a \(3 \times 3\) matrix ⋮ Dynamical systems of operators induced by scaled hypercomplex rings ⋮ Spectral analysis of equations over quaternions ⋮ Operators induced by certain hypercomplex systems ⋮ The minimal polynomial of some matrices via quaternions ⋮ On the global interpolation of motion ⋮ Quaternion involutions and anti-involutions ⋮ Hamilton and Jacobi come full circle: Jacobi algorithms for structured Hamiltonian eigenproblems ⋮ Multi-variable quaternionic spectral analysis

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