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Matrices over Quaternion Algebras - MaRDI portal

Matrices over Quaternion Algebras (Q6117603)

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scientific article; zbMATH DE number 7806657

Language	Label	Description	Also known as
English	Matrices over Quaternion Algebras	scientific article; zbMATH DE number 7806657

Statements

scholarly article

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Matrices over Quaternion Algebras (English)

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10.1007/16618_2023_46

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Matrix and Operator Equations and Applications

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publication date

19 February 2024

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

quaternions

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biquaternions

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matrix equations

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/16618_2023_46

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Fibonacci generalized quaternions

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An Iterative algorithm for $\eta$-(anti)-Hermitian least-squares solutions of quaternion matrix equations

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MUSIC Algorithm for Vector-Sensors Array Using Biquaternions

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Commutative hypercomplex numbers and functions of hypercomplex variable: a matrix study

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An introduction to commutative quaternions

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The solution of the matrix equations \(AXB-CXD=E\) and \((YA-DZ,YC- BZ)=(E,F)\)

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Positive and real-positive solutions to the equation<i>axa</i>*=<i>c</i>in<i>C</i>*-algebras

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Re-nnd SOLUTIONS OF THE MATRIX EQUATION <i>AXB</i>=<i>C</i>

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On eigenvalues of split quaternion matrices

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On complex split quaternion matrices

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Two-sided linear split quaternionic equations with<i>n</i>unknowns

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A different polar representation for generalized and generalized dual quaternions

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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 \(q \mapsto \hat{q}\)

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Reduced biquaternion canonical transform, convolution and correlation

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A real quaternion matrix equation with applications

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A generalization of the complex Autonne–Takagi factorization to quaternion matrices

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The matrix equation \(AXB-GXB=E\) over the quaternion field

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Para-Hermitian and paraquaternionic manifolds

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Generalized quaternions and their algebraic properties

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

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On solutions of the matrix equations \(X\)-\(AXB\)=\(C\) and \(A{\overline{X}}B\)=\(C\)

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Algebraic techniques for Schrödinger equations in split quaternionic mechanics

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Consimilarity and quaternion matrix equations \(AX -\hat{X}B = C\), \(X - A\hat{X}B = C\)

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Commutative quaternion matrices

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Consimilarity of Commutative Quaternion Matrices

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On the Consimilarity of Split Quaternions and Split Quaternion Matrices

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The \(\eta \)-anti-Hermitian solution to some classic matrix equations

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Consistency of split quaternion matrix equations \(AX^{\star }-XB=CY+D\) and \(X-AX^\star B=CY+D\)

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Least squares <i>X</i>=±<i>X</i><sup><i>η</i>*</sup> solutions to split quaternion matrix equation <i>A</i><i>X</i><i>A</i><sup><i>η</i>*</sup>=<i>B</i>

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On the split quaternion matrix equation \(AX=B\)

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Real representation approach to quaternion matrix equation involving \(\varphi \)-Hermicity

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On the matrix algebra of elliptic biquaternions

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\(p\)-trigonometric approach to elliptic biquaternions

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Commutative Reduced Biquaternions and Their Fourier Transform for Signal and Image Processing Applications

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Computational line geometry

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Solution to a system of real quaternion matrix equations encompassing \(\eta\)-Hermicity

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The Equations AX - YB = C and AX - XB = C in Matrices

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Determination of the biquaternion divisors of zero, including the idempotents and nilpotents.

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Computational Methods for Linear Matrix Equations

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Explicit solutions to the quaternion matrix equations<i>X</i>−<i>AXF</i>=<i>C</i>and<i>X</i>−<i>A[Xtilde]</i><i>F</i>=<i>C</i>

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Quaternion Algebras

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Algebraic techniques for least squares problem over generalized quaternion algebras: A unified approach in quaternionic and split quaternionic theory

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Two algebraic methods for least squares L-structured and generalized L-structured problems of the commutative quaternion Stein matrix equation

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The matrix equation \(X-AXB=C\) and an analogue of Roth's theorem

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The Re-nonnegative definite solutions to the matrix inverse problem \(AX=B\)

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On elliptic biquaternion matrices

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The generalized quaternion matrix equation <i>A</i><i>X</i><i>B</i>+<i>C</i><i>X</i><sup>⋆</sup><i>D</i>=<i>E</i>

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On Hermitian solutions of the split quaternion matrix equation \(AXB+CXD=E\)

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The rank-constrained Hermitian nonnegative-definite and positive-definite solutions to the matrix equation \(AXA^{\ast}=B\)

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Special least squares solutions of the quaternion matrix equation \(AXB+CXD=E\)

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The exact solution of a system of quaternion matrix equations involving \(\eta\)-Hermicity

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${\cal H}$-Representation and Applications to Generalized Lyapunov Equations and Linear Stochastic Systems

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Algebraic methods for least squares problem in split quaternionic mechanics

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The *congruence class of the solutions of some matrix equations

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Sitelinks

Mathematics(1 entry)

mardi Publication:6117603

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