Explicit solutions to the quaternion matrix equationsX−AXF=CandX−A[Xtilde]F=C
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Publication:4903522
DOI10.1080/00207160.2012.666346zbMath1255.15004OpenAlexW2086267332MaRDI QIDQ4903522
Caiqin Song, Qing-Bing Liu, Guo-Liang Chen
Publication date: 22 January 2013
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00207160.2012.666346
Matrix equations and identities (15A24) Operator theory over fields other than (mathbb{R}), (mathbb{C}) or the quaternions; non-Archimedean operator theory (47S10) Linear equations (linear algebraic aspects) (15A06)
Related Items (24)
An efficient method for least-squares problem of the quaternion matrix equationX-AX̂B=C ⋮ A general method for solving linear matrix equations of elliptic biquaternions with applications ⋮ Determinantal representations of general and (skew-)Hermitian solutions to the generalized Sylvester-type quaternion matrix equation ⋮ Solutions to matrix equations \(X - AXB = CY + R\) and \(X - A\hat{X}B = CY + R\) ⋮ Two algebraic methods for least squares L-structured and generalized L-structured problems of the commutative quaternion Stein matrix equation ⋮ Parametric Solutions to the Generalized Discrete Yakubovich-Transpose Matrix Equation ⋮ Numerical algorithms for solving the least squares symmetric problem of matrix equation AXB + CXD = E ⋮ Least squares η-bi-Hermitian problems of the quaternion matrix equation (AXB,CXD) = (E,F) ⋮ Closed-form solutions to the nonhomogeneous Yakubovich-transpose matrix equation ⋮ On Hermitian solutions of the split quaternion matrix equation \(AXB+CXD=E\) ⋮ Matrices over Quaternion Algebras ⋮ Direct methods onη‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F) ⋮ 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 \(q \mapsto \hat{q}\) ⋮ Cramer's rules for Sylvester quaternion matrix equation and its special cases ⋮ Consimilarity and quaternion matrix equations \(AX -\hat{X}B = C\), \(X - A\hat{X}B = C\) ⋮ Least squares Hermitian solution of the complex matrix equation \(AXB+CXD=E\) with the least norm ⋮ Consistency of split quaternion matrix equations \(AX^{\star }-XB=CY+D\) and \(X-AX^\star B=CY+D\) ⋮ A quaternion matrix equation with two different restrictions ⋮ L-structured quaternion matrices and quaternion linear matrix equations ⋮ The least square solution with the least norm to a system of quaternion matrix equations ⋮ On solutions of the generalized Stein quaternion matrix equation ⋮ An efficient algorithm for the generalized \((P,Q)\)-reflexive solution to a quaternion matrix equation and its optimal approximation ⋮ On Hermitian solutions of the reduced biquaternion matrix equation (AXB,CXD) = (E,G) ⋮ Least-squares problem for the quaternion matrix equationAXB+CYD=Eover different constrained matrices
Cites Work
- Quaternion singular value decomposition based on bidiagonalization to a real or complex matrix using quaternion Householder transformations
- Jacobi method for quaternion matrix singular value decomposition
- Least squares Hermitian solution of the matrix equation \((AXB,CXD)=(E,F)\) with the least norm over the skew field of quaternions
- Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing
- A quaternion QR-algorithm
- A canonical form for pencils of matrices with applications to asymptotic linear programs
- A Faddeev sequence method for solving Lyapunov and Sylvester equations
- On solutions of matrix equation \(XF-AX=C\) and \(XF-A\widetilde{X}=C\) over quaternion field
- Distribution and estimation for eigenvalues of real quaternion matrices
- On a solution of the quaternion matrix equation \(X-A \widetilde{X} B=C\) and its application
- Further remarks on the Cayley-Hamilton theorem and Leverrier's method for the matrix pencil<tex>(sE - A)</tex>
- Quaternions and matrices of quaternions
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