Some properties of submatrices in a solution to the matrix equations \(AX=C, XB=D\)

DOI10.1007/s12190-008-0192-7zbMath1186.15013OpenAlexW2044105334MaRDI QIDQ1034951

Yong Hui Liu

Publication date: 9 November 2009

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-008-0192-7

zbMATH Keywords

independencesystemmatrix equationsminimal rankmaximal rankpartitioned matricessubmatrices

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (3)

Extremal ranks of submatrices in an Hermitian solution to the matrix equation \(AXA^{*}=B\) with applications ⋮ Ranks of Submatrices in a Solution to a Consistent System of Linear Quaternion Matrix Equations with Applications ⋮ The solution of the matrix equation \(AXB=D\) and The system of matrix equations \(AX=C\), \(XB=D\) with \(X^*X=I_p\)

Cites Work

• The matrix equations \(AX=C\), \(XB=D\)
• Ranks of least squares solutions of the matrix equation \(AXB=C\)
• The maximal and minimal ranks of \(A - BXC\) with applications
• Generalized inverses: theory and computations
• Ranks of solutions of the linear matrix equation \(AX + YB = C\)
• Linear maps preserving pairs of Hermitian matrices on which the rank is additive and applications
• More on extremal ranks of the matrix expressions A  − BX  ± X ^* B ^* with statistical applications
• Extremal Ranks of Some Symmetric Matrix Expressions with Applications
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