Rank minimization of generalized Sylvester equations over Bézout domains

DOI10.1016/j.laa.2012.11.012zbMath1283.15045OpenAlexW2122363180MaRDI QIDQ2637174

Harald K. Wimmer, Naoharu Ito

Publication date: 19 February 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2012.11.012

zbMATH Keywords

generalized inversesBézout domainrank minimizationgeneralized Sylvester equationRoth's equivalence theorem

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (1)

The equivalence canonical form of five quaternion matrices with applications to imaging and Sylvester-type equations

Cites Work

• Almost non-interacting control by measurement feedback
• The matrix equation \(AX-YB=C\)
• The minimal rank of the matrix expression \(A-BX-YC\)
• THE GENERALIZED SYLVESTER MATRIX EQUATION, RANK MINIMIZATION AND ROTH’S EQUIVALENCE THEOREM
• On Generalized Inverses of Matrices over Principal Ideal Rings
• The generalized Sylvester equation in polynomial matrices
• The Polynomial Equation $QQ_c + RP_c = \Phi $ with Application to Dynamic Feedback
• The Equations AX - YB = C and AX - XB = C in Matrices
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