Maximum and minimum ranks and inertias of the Hermitian parts of the least rank solution of the matrix equation \(AXB = C\)

DOI10.3934/naco.2020016zbMath1479.15010OpenAlexW3004852586MaRDI QIDQ2061322

Sihem Guerarra

Publication date: 13 December 2021

Published in: Numerical Algebra, Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/naco.2020016

zbMATH Keywords

rankmatrix equationMoore-Penrose generalized inverseinertiasleast-rank solution

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03) Numerical methods for matrix equations (65F45) Applications of generalized inverses (15A10)

Cites Work

• Maximization and minimization of the rank and inertia of the Hermitian matrix expression \(A-BX-(BX)^{*}\) with applications
• Ranks of least squares solutions of the matrix equation \(AXB=C\)
• Equalities and inequalities for inertias of Hermitian matrices with applications
• The maximal and minimal ranks of \(A - BXC\) with applications
• Nonnegative-definite and positive-definite solutions to the matrix equation \(\mathbb{A}\times\mathbb{A}^*=\mathbb{B}\) -- revisited
• The maximal and minimal ranks of some expressions of generalized inverses of matrices
• Generalized inverses. Theory and applications.
• Positive and negative definite submatrices in an Hermitian least rank solution of the matrix equation \(AXA^*=B\)
• Relations between least-squares and least-rank solutions of the matrix equation \(AXB=C\)
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
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