Cramer's rule for some quaternion matrix equations
From MaRDI portal
Publication:606728
DOI10.1016/j.amc.2010.07.003zbMath1205.15026arXiv1004.4380OpenAlexW2040568630MaRDI QIDQ606728
Publication date: 18 November 2010
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1004.4380
inverse matrixCramer's rulequaternion matrix equationnoncommutative determinantquaternion skew field
Determinants, permanents, traces, other special matrix functions (15A15) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24)
Related Items
Linear quaternion-valued difference equations: Representation of solutions, controllability, and observability ⋮ The least squares bisymmetric solution of quaternion matrix equation \(AXB = C\) ⋮ The least-squares solution with the least norm to a system of tensor equations over the quaternion algebra ⋮ On some spectral properties of large self-dual dilute quaternion random matrices ⋮ Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations ⋮ On Hermitian solutions of the split quaternion matrix equation \(AXB+CXD=E\) ⋮ Boundary value problems of quaternion-valued differential equations: solvability and Green's function ⋮ Cramer's rules for some Hermitian coquaternionic matrix equations ⋮ Analogs of Cramer's rule for the minimum norm least squares solutions of some matrix equations ⋮ Direct methods onη‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F) ⋮ Condensed Cramer rule for some restricted quaternion linear equations ⋮ Unnamed Item ⋮ Determinantal representation of the generalized inverses over the quaternion skew field with applications ⋮ The column and row immanants over a split quaternion algebra ⋮ New results on condensed Cramer's rule for the general solution to some restricted quaternion matrix equations ⋮ Conjugate gradient-like algorithms for constrained operator equation related to quadratic inverse eigenvalue problems ⋮ On the convergence of conjugate direction algorithm for solving coupled Sylvester matrix equations ⋮ Cramer’s rule over quaternions and split quaternions: A unified algebraic approach in quaternionic and split quaternionic mechanics ⋮ Cramer's rule for the general solution to a restricted system of quaternion matrix equations ⋮ Cramer rule for the unique solution of restricted matrix equations over the quaternion skew field ⋮ L-structured quaternion matrices and quaternion linear matrix equations ⋮ On the second Lyapunov method for quaternionic differential equations ⋮ Bott-Duffin inverse over the quaternion skew field with applications ⋮ Explicit determinantal representation formulas of \(W\)-weighted Drazin inverse solutions of some matrix equations over the quaternion skew field ⋮ On Hermitian solutions of the reduced biquaternion matrix equation (AXB,CXD) = (E,G) ⋮ Determinantal representations of the solutions to systems of generalized Sylvester equations ⋮ Least-squares problem for the quaternion matrix equationAXB+CYD=Eover different constrained matrices ⋮ Unnamed Item ⋮ Cramer's rule for a system of quaternion matrix equations with applications ⋮ Cramer's rules for various solutions to some restricted quaternionic linear systems ⋮ The Moore-Penrose inverses of matrices over quaternion polynomial rings
Cites Work
- Unnamed Item
- On solutions of the matrix equations \(X\)-\(AXB\)=\(C\) and \(A{\overline{X}}B\)=\(C\)
- The common solution to six quaternion matrix equations with applications
- The general solution to a system of real quaternion matrix equations
- Cramer's rule for quaternionic systems of linear equations
- Definition of determinant and cramer solutions over the quaternion field
- Ranks of Solutions of the Matrix Equation AXB = C
This page was built for publication: Cramer's rule for some quaternion matrix equations
