Some properties of submatrices in a solution to the matrix equation \(AXB=C\) with applications

DOI10.1016/j.jfranklin.2009.02.013zbMath1168.15307OpenAlexW2027856933MaRDI QIDQ834154

Yongge Tian

Publication date: 19 August 2009

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2009.02.013

zbMATH Keywords

generalized inversegeneral solutionslinear matrix equationsmaximal and minimal rankssubmatricesindependence of solutionsrank formulas

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 (6)

Ranks of Submatrices in a Solution to a Consistent System of Linear Quaternion Matrix Equations with Applications ⋮ New solution bounds for the continuous algebraic Riccati equation ⋮ Algorithm for inequality-constrained least squares problems ⋮ Solutions with special structure to the linear matrix equation \(AX=B\) ⋮ Least squares solutions with special structure to the linear matrix equation \(AXB = C\) ⋮ The \(\{P,Q,k+1\}\)-reflexive solution of matrix equation \(AXB=C\)

Cites Work

• Generalized inverses of partitioned matrices useful in statistical applications
• The minimal rank of the matrix expression \(A-BX-YC\)
• Using rank formulas to characterize equalities for Moore-Penrose inverses of matrix products.
• Completing triangular block matrices with maximal and minimal ranks
• The maximal and minimal ranks of some expressions of generalized inverses of matrices
• Upper and lower bounds for ranks of matrix expressions using generalized inverses
• Generalized inverses. Theory and applications.
• The solvability of two linear matrix equations
• Rank equalities related to outer inverses of matrices and applications
• The Equation $AXB + CYD = E$ over a Principal Ideal Domain
• Ranks of Solutions of the Matrix Equation AXB = C
• The Minimum Rank of a 3 × 3 Partial Block Matrix
• When does rank(ABC) = rank(AB) + rank(BC) - rank(B) hold?
• Rank equalities for idempotent and involutory matrices
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