The minimal rank of the matrix expression \(A-BX-YC\)

zbMath1032.15001MaRDI QIDQ1407444

Yongge Tian

Publication date: 10 March 2004

Published in: Missouri Journal of Mathematical Sciences (Search for Journal in Brave)

zbMATH Keywords

linear matrix equationminimum rankrank of matrix

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (13)

Some properties of submatrices in a solution to the matrix equation \(AXB=C\) with applications ⋮ Rank minimization of generalized Sylvester equations over Bézout domains ⋮ Extreme ranks of the solution to a consistent system of linear quaternion matrix equations with an application ⋮ Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications ⋮ Minimal ranks of some quaternion matrix expressions with applications ⋮ The real and complex Hermitian solutions to a system of quaternion matrix equations with applications ⋮ Ranks of least squares solutions of the matrix equation \(AXB=C\) ⋮ Ranks of solutions of the linear matrix equation \(AX + YB = C\) ⋮ Alternating Direction Method for a Class of Sylvester Matrix Equations with Linear Matrix Inequality Constraint ⋮ Relations between matrix sets generated from linear matrix expressions and their applications ⋮ Rank equalities for idempotent matrices with applications. ⋮ Least squares solutions with special structure to the linear matrix equation \(AXB = C\) ⋮ Upper and lower bounds for ranks of matrix expressions using generalized inverses

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