Extremal ranks of a quadratic matrix expression with applications

DOI10.1080/03081081003774268zbMath1220.15006OpenAlexW2095269522MaRDI QIDQ3006573

Yongge Tian

Publication date: 20 June 2011

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

Full work available at URL: https://doi.org/10.1080/03081081003774268

zbMATH Keywords

Schur complementgeneralized inversematrix equationlinear matrix expressionquadratic matrix expressionrank formulae

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

Necessary and sufficient conditions for nonlinear matrix identities to always hold ⋮ Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications ⋮ Closed-form formulas for calculating the max-min ranks of a triple matrix product composed by generalized inverses ⋮ Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method ⋮ How to establish exact formulas for calculating the max–min ranks of products of two matrices and their generalized inverses ⋮ Inequalities for ranks of matrix expressions involving generalized inverses ⋮ Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications ⋮ An invariance property related to the mixed-type reverse order laws

Cites Work

• What are Schur complements, anyway?
• The lower order of lower triangular operators and minimal rank extensions
• Completing triangular block matrices with maximal and minimal ranks
• Minimal rank completions for block matrices
• 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
• Minimum rank completions
• The Restricted Singular Value Decomposition: Properties and Applications
• Minimal rank completions of partial banded matrices
• The Minimum Rank of a 3 × 3 Partial Block Matrix
• Generalized Inverse Formulas Using the Schur Complement
• Extremal Ranks of Some Symmetric Matrix Expressions with Applications
• Unicity of minimal rank completions for tri-diagonal partial block matrices

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