Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics

DOI10.1063/1.4928935zbMath1327.15014OpenAlexW1595874081MaRDI QIDQ2945516

Zhaozhong Zhang, Zi-Wu Jiang, Tong-Song Jiang

Publication date: 11 September 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4928935

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Alternative quantum mechanics (including hidden variables, etc.) (81Q65) General models, approaches, and methods in mechanics of particles and systems (70G99)

Related Items

On singular value decomposition for split quaternion matrices and applications in split quaternionic mechanics ⋮ Matrices over Quaternion Algebras ⋮ Two novel numerical methods for the diagonalisation of a reduced biquaternion matrix in the reduced biquaternionic algebra ⋮ Algebraic techniques for Schrödinger equations in split quaternionic mechanics ⋮ Consistency of split quaternion matrix equations \(AX^{\star }-XB=CY+D\) and \(X-AX^\star B=CY+D\) ⋮ On the split quaternion matrix equation \(AX=B\) ⋮ A complex structure-preserving algorithm for split quaternion matrix \textit{LDU} decomposition In split quaternion mechanics ⋮ Elementary transformation and its applications for split quaternion matrices ⋮ A novel algebraic approach for the Schrödinger equation in split quaternionic mechanics

Cites Work

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• Some algebraic and analytical properties of coquaternion algebra
• The roots of a split quaternion
• Non-Hermitian Quantum Mechanics
• On complexified mechanics and coquaternions
• Algebraic methods for diagonalization of a quaternion matrix in quaternionic quantum theory
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• SPLIT QUATERNIONS AND ROTATIONS IN SEMI EUCLIDEAN SPACE E⁴₂

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