Singular, nonsingular, and bounded rank completions of ACI-matrices

DOI10.1016/j.laa.2010.05.018zbMath1205.15042OpenAlexW2015117287MaRDI QIDQ5962295

Richard A. Brualdi, Xingzhi Zhan, Ze-Jun Huang

Publication date: 21 September 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2010.05.018

zbMATH Keywords

matrix completionrankdeterminantpartial matrixmatrices over polynomial ringsaffine column independent matrixnonsingular

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Matrices over function rings in one or more variables (15A54) Vector spaces, linear dependence, rank, lineability (15A03) Matrix completion problems (15A83)

Related Items (13)

ACI-matrices of constant rank over arbitrary fields ⋮ On the maximum rank of completions of entry pattern matrices ⋮ Partial matrices whose completions all have the same rank ⋮ Nonsingular ACI-matrices over integral domains ⋮ Partial matrices all of whose completions have the same spectrum ⋮ ACI-matrices all of whose completions have the same rank ⋮ On completions of symmetric and antisymmetric block diagonal partial matrices ⋮ Characterization of full rank ACI-matrices over fields ⋮ Symmetric matrices whose entries are linear functions ⋮ Partial matrices of constant rank ⋮ The WST-decomposition for partial matrices ⋮ Partial matrices whose completions have ranks bounded below ⋮ Almost-nonsingular entry pattern matrices

Cites Work

• König's theorem and bimatroids
• A determinantal version of the frobenius-könig theorem
• The Power of Convex Relaxation: Near-Optimal Matrix Completion
• Matrices and matroids for systems analysis
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