A complex structure-preserving algorithm for the full rank decomposition of quaternion matrices and its applications

DOI10.1007/s11075-022-01310-1zbMath1505.65157OpenAlexW4280654432WikidataQ114224273 ScholiaQ114224273MaRDI QIDQ2098791

Dong Zhang, Gang Wang, Tong-Song Jiang, Vasiliy I. Vasil'ev

Publication date: 22 November 2022

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-022-01310-1

zbMATH Keywords

complex representationquaternion matrixsparse representation classificationcomplex structure-preserving algorithmfull rank decomposition

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (2)

\(\mathcal{L_C}\) structure-preserving method based on semi-tensor product of matrices for the QR decomposition in quaternionic quantum theory ⋮ A complex structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix and its applications

Uses Software

• Quaternion

Cites Work

• Unnamed Item
• A fast structure-preserving method for computing the singular value decomposition of quaternion matrices
• Real structure-preserving algorithms of Householder based transformations for quaternion matrices
• A structure-preserving method for the quaternion LU decomposition in quaternionic quantum theory
• Jacobi method for quaternion matrix singular value decomposition
• A structure-preserving algorithm for the quaternion Cholesky decomposition
• Parallel Gaussian elimination on an MIMD computer
• Universal numerical algorithms and their software implementation
• A real structure-preserving method for the quaternion LU decomposition, revisited
• A structure-preserving Jacobi algorithm for quaternion Hermitian eigenvalue problems
• On the power method for quaternion right eigenvalue problem
• Quaternionic groups in physics
• A new structure-preserving method for quaternion Hermitian eigenvalue problems
• Full-rank representation of generalized inverse \(A_{T,S}^{(2)}\) and its application
• An algorithm for quaternionic linear equations in quaternionic quantum theory
• Structured tools for structured matrices
• Algebraic techniques for least squares problem over generalized quaternion algebras: A unified approach in quaternionic and split quaternionic theory

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