Ranks of solutions of the linear matrix equation \(AX + YB = C\)

DOI10.1016/j.camwa.2006.05.011zbMath1129.15009OpenAlexW1984130493MaRDI QIDQ2458506

Yong Hui Liu

Publication date: 1 November 2007

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2006.05.011

zbMATH Keywords

generalized inverseminimal rankmaximal rank

Mathematics Subject Classification ID

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

Related Items (19)

On the solvability of generalized Sylvester operator equations ⋮ The minimal rank of matrix expressions with respect to Hermitian matrix-revised ⋮ Solvability conditions and general solution for mixed Sylvester equations ⋮ Extremal ranks of submatrices in an Hermitian solution to the matrix equation \(AXA^{*}=B\) with applications ⋮ The real and complex Hermitian solutions to a system of quaternion matrix equations with applications ⋮ Dual \(r\)-rank decomposition and its applications ⋮ On extremal ranks and least squares solutions subject to a rank restriction ⋮ Systems of coupled generalized Sylvester matrix equations ⋮ Ranks of the common solution to six quaternion matrix equations ⋮ Ranks of least squares solutions of the matrix equation \(AXB=C\) ⋮ Extremal ranks of some nonlinear matrix expressions with applications ⋮ An alternating direction method for nonnegative solutions of the matrix equation \(AX+YB=C\) ⋮ Solutions with special structure to the linear matrix equation \(AX=B\) ⋮ A NOTE ON SOME SYSTEMS OF GENERALIZED SYLVESTER EQUATIONS ⋮ Solving the mixed Sylvester matrix equations by matrix decompositions ⋮ Ranks and the least-norm of the general solution to a system of quaternion matrix equations ⋮ Some properties of submatrices in a solution to the matrix equations \(AX=C, XB=D\) ⋮ Ranks of Hermitian and skew-Hermitian solutions to the matrix equation \(AXA^*=B\) ⋮ Solvability conditions for mixed sylvester equations in rings

Cites Work

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• The solution of the matrix equations \(AXB-CXD=E\) and \((YA-DZ,YC- BZ)=(E,F)\)
• The matrix equation \(AX-YB=C\)
• The minimal rank of the matrix expression \(A-BX-YC\)
• Upper and lower bounds for ranks of matrix expressions using generalized inverses
• Generalized inverses. Theory and applications.
• Roth's Equivalence Problem in Unit Regular Rings
• On the matrix equations $AX - XB = C$ and $AX - YB = C$
• Ranks of Solutions of the Matrix Equation AXB = C
• The Equations AX - YB = C and AX - XB = C in Matrices
• A representation of the general common solution to the matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) with applications

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