Quaternions and matrices of quaternions

1997/01/01 by Fuzhen Zhang · 52 citations
Mathematics · Computer Science · #Algebraic and Geometric Analysis #Matrix Theory and Algorithms #Mathematics and Applications

paper · doi:10.1016/0024-3795(95)00543-9

Cited by

• Bridge the Gaps: Heterogeneous Attributed Graph Clustering via Quaternion Representation Learning
• A Low Rank Quaternion Decomposition Algorithm and Its Application in Color Image Inpainting
• Octonionic Quadratic Equations
• Riemannian Optimization Framework on the Generalized Quaternionic Stiefel Manifold
• DOA and Polarization Estimation for Non-Circular Signals in 3-D Millimeter Wave Polarized Massive MIMO Systems
• Low Rank Support Quaternion Matrix Machine
• Beyond real: Investigating the role of complex numbers in self-testing
• Weyl distributions, spectral properties, and circulant approximation results for quaternion block multilevel Toeplitz matrix sequences
• Trace map, Cayley transform and LS category of Lie groups
• The Power Method for Non-Hermitian Dual Quaternion Matrices
• Inverse eigenproblems and approximation problems for the generalized reflexive and antireflexive matrices with respect to a pair of generalized reflection matrices
• Classification of Quaternionic Projective Transformations by Equicontinuity Regions
• Continuity of total signature maps for Azumaya algebras with involution
• Characterizing the Universal Rigidity of Generic Tensegrities
• Low-rank quaternion tensor completion for recovering color videos and images
• Generalized singular value decompositions of dual quaternion matrices and beyond
• InvSim algorithm for pre-computing airplane flight controls in limited-range autonomous missions, and demonstration via double-roll maneuver of Mirage III fighters
• A fragile zero-watermarking method based on dual quaternion matrix decomposition
• Quaternion higher-order singular value decomposition and its applications in color image processing
• Roots and right factors of polynomials and left eigenvalues of matrices over Cayley-Dickson algebras
• Eigenvalues and Singular Values of Dual Quaternion Matrices
• Quaternions in Signal and Image Processing: A comprehensive and objective overview
• Moore-Penrose inverse of quaternion tensors via M-product with applications in color image classification
• Real linear quaternionic operators
• Tensor decompositions and tensor equations over quaternion algebra
• Observer Design over Hypercomplex Quaternions
• Cowen-Douglas operators on quaternionic Hilbert spaces
• The solvability conditions and exact solutions to some quaternion tensor systems
• Some remarks and properties of algebras obtained by the Cayley-Dickson\n process
• Maximum principles for matrix-valued regular functions of a quaternionic variable
• Quaternion Toeplitz matrices and their fundamental properties
• Left eigenvalues of 2× 2 symplectic matrices
• A Structure-Preserving One-Sided Jacobi Method for Computing the SVD of a Quaternion Matrix
• Eigenvalues and Singular Value Decomposition of Dual Complex Matrices
• Iterative Methods for Computing the Moore-Penrose Pseudoinverse of Quaternion Matrices, with Applications
• Full Quaternion Representation of Color images: A Case Study on QSVD-based Color Image Compression
• Quaternionic MUBs in H² and their reflection symmetries
• An elementary classification of the quaternionic reflection groups of rank two
• Split Quaternion Matrix Representation of Dual Split Quaternions and Their Matrices
• Shape-from-Template with Generalised Camera
• Algebraic structures spanned by differential-like operators on toy Fock spaces
• Quaternion-Based Robust PCA for Efficient Moving Target Detection and Background Recovery in Color Videos
• Systems of four coupled one sided Sylvester-type real quaternion matrix equations and their applications
• Pass-efficient Randomized Algorithms for Low-rank Approximation of Quaternion Matrices
• Quaternion-Domain Super MDS for Robust 3D Localization
• A Note on Quaternion Skew-Symmetric Matrices
• Semidefinite descriptions of separable matrix cones
• Riemannian Gaussian distributions on the space of positive-definite\n quaternion matrices
• Intrinsic volumes of symmetric cones
• A topological approach to left eigenvalues of quaternionic matrices
• Constrained low-rank quaternion approximation for color image denoising by bilateral random projections
• Quaternion [wikipedia]