The maximal and minimal ranks of matrix expression with applications

DOI10.1186/1029-242X-2012-54zbMath1275.15002OpenAlexW2163640389WikidataQ59290735 ScholiaQ59290735MaRDI QIDQ371035

Yingying Qin, Shi-Fang Yuan, Zhi-Ping Xiong

Publication date: 20 September 2013

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1029-242x-2012-54

zbMATH Keywords

Schur complementgeneralized inverseminimal rankmaximal rankmatrix expressionrank equality

Mathematics Subject Classification ID

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

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Cites Work

• Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix
• Using rank formulas to characterize equalities for Moore-Penrose inverses of matrix products.
• Completing triangular block matrices with maximal and minimal ranks
• Upper and lower bounds for ranks of matrix expressions using generalized inverses
• Extremal ranks of submatrices in an Hermitian solution to the matrix equation \(AXA^{*}=B\) with applications
• More on maximal and minimal ranks of Schur complements with applications
• More on extremal ranks of the matrix expressions A  − BX  ± X ^* B ^* with statistical applications
• Minimum rank completions
• The Equations A^TX\pm X^TA=B
• Minimal rank completions of partial banded matrices
• Ranks of Solutions of the Matrix Equation AXB = C
• The Minimum Rank of a 3 × 3 Partial Block Matrix
• Extremal Ranks of Some Symmetric Matrix Expressions with Applications
• Unicity of minimal rank completions for tri-diagonal partial block matrices

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