Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations
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Publication:5866195
DOI10.2298/FIL2008601RzbMath1499.15054OpenAlexW3131208469MaRDI QIDQ5866195
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Publication date: 13 June 2022
Published in: Filomat (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2298/fil2008601r
Moore-Penrose inverseCramer's rulequaternion matrixnoncommutative determinantSylvester-type matrix equation
Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24)
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Cites Work
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- Determinantal representations of the Drazin inverse over the quaternion skew field with applications to some matrix equations
- Constraint generalized Sylvester matrix equations
- Condensed Cramer rule for some restricted quaternion linear equations
- On the Hermitian solutions to a system of adjointable operator equations
- 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 \(q \mapsto \hat{q}\)
- New results on condensed Cramer's rule for the general solution to some restricted quaternion matrix equations
- Minimal ranks of some quaternion matrix expressions with applications
- Augmented second-order statistics of quaternion random signals
- On the unitary diagonalisation of a special class of quaternion matrices
- Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation \(A_1X_1B_1+A_2X_2B_2=C\)
- The solvability conditions for the inverse eigenproblems of symmetric and generalized centro-symmetric matrices and their approximations
- The exact solution of a system of quaternion matrix equations involving \(\eta\)-Hermicity
- Generalized inverses over integral domains
- On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\)
- Ranks and the least-norm of the general solution to a system of quaternion matrix equations
- Perturbation analysis and condition numbers of symmetric algebraic Riccati equations
- Almost non-interacting control by measurement feedback
- On solutions of matrix equation \(AXB+CYD=F\)
- Quaternionic determinants
- The constrained solutions of two matrix equations
- The Sylvester equation and approximate balanced reduction
- Determinantal representations of solutions to systems of quaternion matrix equations
- Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field
- Solution to a system of real quaternion matrix equations encompassing \(\eta\)-Hermicity
- A constraint system of generalized Sylvester quaternion matrix equations
- Determinantal representations of solutions and Hermitian solutions to some system of two-sided quaternion matrix equations
- A system of matrix equations with five variables
- Recurrent neural network for computing the \(W\)-weighted Drazin inverse
- Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore-Penrose inverse
- Generalized inverses: theory and computations
- Explicit determinantal representation formulas for the solution of the two-sided restricted quaternionic matrix equation
- Explicit determinantal representation formulas of \(W\)-weighted Drazin inverse solutions of some matrix equations over the quaternion skew field
- A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
- Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations
- Effective condition numbers and small sample statistical condition estimation for the generalized Sylvester equation
- Cramer's rules for Sylvester quaternion matrix equation and its special cases
- The solution to matrix equation \(AX+X^TC=B\)
- The general solution of quaternion matrix equation having \(\eta \)-skew-Hermicity and its Cramer's rule
- Least-norm of the general solution to some system of quaternion matrix equations and its determinantal representations
- Cramer's rule for a system of quaternion matrix equations with applications
- Generalization of Roth's solvability criteria to systems of matrix equations
- Cramer's rules of \(\eta \)-(skew-)Hermitian solutions to the quaternion Sylvester-type matrix equations
- The \(\eta \)-anti-Hermitian solution to some classic matrix equations
- Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle
- Determinantal representations of general and (skew-)Hermitian solutions to the generalized Sylvester-type quaternion matrix equation
- A common solution to a pair of linear matrix equations over a principal ideal domain
- Theη-bihermitian solution to a system of real quaternion matrix equations
- Representations and properties of theW-Weighted Drazin inverse
- A generalization of the complex Autonne–Takagi factorization to quaternion matrices
- Some matrix equations with applications†
- An Iterative algorithm for $\eta$-(anti)-Hermitian least-squares solutions of quaternion matrix equations
- On Perhermitian Matrices
- Analogs of the adjoint matrix for generalized inverses and corresponding Cramer rules
- Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
- Finite quaternionic matrix groups
- The quaternionic determinant
- The Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes
- Quaternion-MUSIC for vector-sensor array processing
- Quaternions, Spinors, and Surfaces
- The matrix equationAXB+CYD=Eover a simple artinian ring
- Mixed, componentwise condition numbers and small sample statistical condition estimation of Sylvester equations
- Optimization of a nonlinear Hermitian matrix expression with application
- Coupled Sylvester-type Matrix Equations and Block Diagonalization
- Gradient based iterative algorithms for solving a class of matrix equations
- A real quaternion matrix equation with applications
- Das verallgemeinerte Inverse einer Matrix, deren Elemente einem beliebigen Körper angehören.
- Determinantal representations of solutions to systems of two-sided quaternion matrix equations
- Quaternions and matrices of quaternions