The Equation $AXB + CYD = E$ over a Principal Ideal Domain
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Publication:3977066
DOI10.1137/0612044zbMath0742.15006OpenAlexW2115576014MaRDI QIDQ3977066
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Publication date: 25 June 1992
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0612044
Linear systems in control theory (93C05) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24) Algebraic methods (93B25)
Related Items (30)
Hermitian solutions to the system of operator equations T_iX=U_i. ⋮ Some properties of submatrices in a solution to the matrix equation \(AXB=C\) with applications ⋮ The Minimum Rank of a 3 × 3 Partial Block Matrix ⋮ A simple method for solving matrix equations \(AXB = D\) and \(GXH = C\) ⋮ An iterative method for the symmetric and skew symmetric solutions of a linear matrix equation \(AXB+CYD=E\) ⋮ Alternating direction method for generalized Sylvester matrix equation \(AXB + CYD = E\) ⋮ Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications ⋮ Theη-bihermitian solution to a system of real quaternion matrix equations ⋮ The least squares problem of the matrix equation \(A_1X_1B^T_1+A_2X_2B^T_2=T\) ⋮ The matrix equationAXB+CYD=Eover a simple artinian ring ⋮ Least squares η-bi-Hermitian problems of the quaternion matrix equation (AXB,CXD) = (E,F) ⋮ The maximal and minimal ranks of a quaternion matrix expression with applications ⋮ A simultaneous decomposition for seven matrices with applications ⋮ The solvability of two linear matrix equations ⋮ Matrix equation \(AXB=E\) with \(PX=sXP\) constraint ⋮ A system of matrix equations with five variables ⋮ The complete equivalence canonical form of four matrices over an arbitrary division ring ⋮ \(P\)-(skew)symmetric common solutions to a pair of quaternion matrix equations ⋮ An iterative algorithm for a least squares solution of a matrix equation ⋮ The matrix nearness problem associated with the quaternion matrix equation \(AXA^H+BYB^H=C\) ⋮ Analytical best approximate Hermitian and generalized skew-Hamiltonian solution of matrix equation \(AXA^{\mathrm{H}}+CYC^{\mathrm{H}}=F\) ⋮ Matrix equations over \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices ⋮ Ranks of submatrices in (skew-)Hermitian solutions to a quaternion matrix equation ⋮ A computational framework of gradient flows for general linear matrix equations ⋮ Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices ⋮ On the weighted least-squares, the ordinary least-squares and the best linear unbiased estimators under a restricted growth curve model ⋮ On consistency, natural restrictions and estimability under classical and extended growth curve models ⋮ A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity ⋮ Solvability conditions for mixed sylvester equations in rings ⋮ Some matrix equations with applications†
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