Matrices over Quaternion Algebras

DOI10.1007/16618_2023_46OpenAlexW4377078708MaRDI QIDQ6117603

No author found.

Publication date: 19 February 2024

Published in: Matrix and Operator Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/16618_2023_46

zbMATH Keywords

quaternionsmatrix equationsbiquaternions

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24) Equations involving linear operators, with operator unknowns (47A62) Clifford algebras, spinors (15A66)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fibonacci generalized quaternions
• Commutative quaternion matrices
• Roth's solvability criteria for the matrix equations \(AX-\hat{X}B=C\) and \(X-A\hat{X}B=C\) over the skew field of quaternions with an involutive automorphism \(q \mapsto \hat{q}\)
• Special least squares solutions of the quaternion matrix equation \(AXB+CXD=E\)
• Reduced biquaternion canonical transform, convolution and correlation
• Algebraic methods for least squares problem in split quaternionic mechanics
• An introduction to commutative quaternions
• The exact solution of a system of quaternion matrix equations involving \(\eta\)-Hermicity
• The *congruence class of the solutions of some matrix equations
• The solution of the matrix equations \(AXB-CXD=E\) and \((YA-DZ,YC- BZ)=(E,F)\)
• The matrix equation \(X-AXB=C\) and an analogue of Roth's theorem
• The rank-constrained Hermitian nonnegative-definite and positive-definite solutions to the matrix equation \(AXA^{\ast}=B\)
• Solution to a system of real quaternion matrix equations encompassing \(\eta\)-Hermicity
• \(p\)-trigonometric approach to elliptic biquaternions
• On Hermitian solutions of the split quaternion matrix equation \(AXB+CXD=E\)
• Algebraic techniques for Schrödinger equations in split quaternionic mechanics
• On solutions of the matrix equations \(X\)-\(AXB\)=\(C\) and \(A{\overline{X}}B\)=\(C\)
• The matrix equation \(AXB-GXB=E\) over the quaternion field
• The Re-nonnegative definite solutions to the matrix inverse problem \(AX=B\)
• A different polar representation for generalized and generalized dual quaternions
• Two algebraic methods for least squares L-structured and generalized L-structured problems of the commutative quaternion Stein matrix equation
• On elliptic biquaternion matrices
• Consimilarity and quaternion matrix equations \(AX -\hat{X}B = C\), \(X - A\hat{X}B = C\)
• Consistency of split quaternion matrix equations \(AX^{\star }-XB=CY+D\) and \(X-AX^\star B=CY+D\)
• On the split quaternion matrix equation \(AX=B\)
• Real representation approach to quaternion matrix equation involving \(\varphi \)-Hermicity
• The \(\eta \)-anti-Hermitian solution to some classic matrix equations
• On complex split quaternion matrices
• On eigenvalues of split quaternion matrices
• Commutative hypercomplex numbers and functions of hypercomplex variable: a matrix study
• Para-Hermitian and paraquaternionic manifolds
• Consimilarity of Commutative Quaternion Matrices
• Generalized quaternions and their algebraic properties
• Two-sided linear split quaternionic equations withnunknowns
• Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics
• A generalization of the complex Autonne–Takagi factorization to quaternion matrices
• Computational Methods for Linear Matrix Equations
• An Iterative algorithm for $\eta$-(anti)-Hermitian least-squares solutions of quaternion matrix equations
• Re-nnd SOLUTIONS OF THE MATRIX EQUATION AXB=C
• MUSIC Algorithm for Vector-Sensors Array Using Biquaternions
• On the Consimilarity of Split Quaternions and Split Quaternion Matrices
• Explicit solutions to the quaternion matrix equationsX−AXF=CandX−A[XtildeF=C]
• Algebraic techniques for least squares problem over generalized quaternion algebras: A unified approach in quaternionic and split quaternionic theory
• On the matrix algebra of elliptic biquaternions
• Least squares X=±X^η* solutions to split quaternion matrix equation AXA^η*=B
• Quaternion Algebras
• The generalized quaternion matrix equation AXB+CX^⋆D=E
• A real quaternion matrix equation with applications
• ${\cal H}$-Representation and Applications to Generalized Lyapunov Equations and Linear Stochastic Systems
• Commutative Reduced Biquaternions and Their Fourier Transform for Signal and Image Processing Applications
• Positive and real-positive solutions to the equationaxa*=cinC*-algebras
• The Equations AX - YB = C and AX - XB = C in Matrices
• Computational line geometry
• Determination of the biquaternion divisors of zero, including the idempotents and nilpotents.