A simple method for solving matrix equations \(AXB = D\) and \(GXH = C\)

DOI10.3934/math.2021156OpenAlexW3113857434MaRDI QIDQ2146629

Yongxin Yuan, Hairui Zhang, Huiting Zhang, Lina Liu

Publication date: 17 June 2022

Published in: AIMS Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/math.2021156

zbMATH Keywords

generalized inversematrix equationcommon solutionHermitian solution

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24)

Related Items (1)

The common re-nonnegative definite and re-positive definite solutions to the matrix equations \(A_1XA_1^\ast = C_1\) and \(A_2XA_2^\ast = C_2 \)

Cites Work

• A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem
• An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices
• Singular value and generalized singular value decompositions and the solution of linear matrix equations
• Almost non-interacting control by measurement feedback
• The matrix equation AXB+CYD=E
• The matrix equation \(AX-YB=C\)
• On solutions of matrix equation \(AXB+CYD=F\)
• On the existence of a common solution \(X\) to the matrix equations \(A_{i} XB_{j}\)=\(C_{ij}\), \((i,j){\in}\Gamma\).
• A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
• Generalized inverses. Theory and applications.
• An efficient method for special least squares solution of the complex matrix equation \((AXB,CXD)=(E,F)\)
• The BCR algorithms for solving the reflexive or anti-reflexive solutions of generalized coupled Sylvester matrix equations
• Some identities of extended degenerate \(r\)-central Bell polynomials arising from umbral calculus
• Computing symmetric solutions of general Sylvester matrix equations via Lanczos version of biconjugate residual algorithm
• Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester matrix equations
• A common solution to a pair of linear matrix equations over a principal ideal domain
• The general solutions to some systems of matrix equations
• An efficient iterative method for solving the matrix equationAXB +CYD =E
• The Equation $AXB + CYD = E$ over a Principal Ideal Domain
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• Representations and cramer rules for the solution of a restricted Matrix Equation^∗
• The matrix equationAXB+CYD=Eover a simple artinian ring
• A finite iterative method for solving the generalized Hamiltonian solutions of coupled Sylvester matrix equations with conjugate transpose
• A representation of the general common solution to the matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) with applications
• Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices
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