Quaternions and matrices of quaternions

1997/01/01 by Fuzhen Zhang · 1,112 citations
Computer Science · Mathematics · #Algebra over a field #Algebraic and Geometric Analysis #Dual quaternion #Geometry #Mathematical proof #Mathematics #Mathematics and Applications #Matrix (chemical analysis) #Matrix Theory and Algorithms #Pure mathematics #Quaternion

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

published in Linear Algebra and its Applications 251, 21-57 (Elsevier BV)

openalex publication_date 1997/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 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 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
• Universal kernels via harmonic analysis on Riemannian symmetric spaces
• Structure Preserving Algorithms for Quaternion Outer Inverses with Applications
• Isometries of the quaternionic hyperbolic line
• Jorgensen's inequality for quaternionic hyperbolic n-space
• Riemann slice-domains over quaternions I
• Determinantal representations of the Drazin inverse for Hermitian matrix over the quaternion skew field with applications
• The Moduli Space of Points in the Boundary of Quaternionic Hyperbolic Space
• Fast Alternating Projections on Manifolds Based on Tangent Spaces
• Polar decompositions of quaternion matrices in indefinite inner product spaces
• Color Image Set Recognition Based on Quaternionic Grassmannians
• Signature maps from positive cones on algebras with involution
• On the Efficacy and High-Performance Implementation of Quaternion Matrix Multiplication
• On The Horadam Hybrid Quaternions
• Debiased inference in error-in-variable problems with non-Gaussian measurement error
• Improved power methods for computing eigenvalues of dual quaternion Hermitian matrices
• Kulkarni limit sets for cyclic quaternionic projective groups
• A new method of finding all Roots of simple quaternionic polynomials
• Quaternionic Kittaneh Numerical Radius Inequalities
• A nonlinear analogue of additive commutators
• Matrices over a Hilbert space and their low-rank approximation
• Complex Projection of Quasianti-Hermitian Quaternionic Hamiltonian Dynamics
• Littlewood's algorithm and quaternion matrices
• Boundary interpolation for slice hyperholomorphic Schur functions
• Quaternion Nuclear Norms Over Frobenius Norms Minimization for Robust Matrix Completion
• Split quaternion matrices
• Quaternion Matrix Optimization and The Underlying Calculus
• Some generalizations of the DDVV and BW inequalities
• Quasistationary quaternionic Hamiltonians and complex stochastic maps
• Kubo Ando Means on the Cone of J Hermitian Matrices
• The tensor rank problem over the quaternions
• Character varieties for real forms of classical complex groups
• Quaternionic Wiener Algebras, Factorization and Applications
• The quaternionic second weighted zeta function of a graph and the Study determinant
• Quaternion Non-Negative Matrix Factorization: Definition, Uniqueness, and Algorithm
• Generic Steady State Bifurcations in Monoid Equivariant Dynamics with Applications in Homogeneous Coupled Cell Systems
• The row left rank of quaternion unit gain graphs in terms of pendant vertices
• Quaternionic quantum theory admits universal dynamics only for two-level systems
• Cayley–Hamilton theorem [wikipedia]
• Quaternion [wikipedia]
• DOA and Polarization Estimation Using an Electromagnetic Vector Sensor Uniform Circular Array Based on the ESPRIT Algorithm. [europepmc]
• Comparison of two SVD-based color image compression schemes. [europepmc]
• InvSim algorithm for pre-computing airplane flight controls in limited-range autonomous missions, and demonstration via double-roll maneuver of Mirage III fighters. [europepmc]