A proof of the \(T_n\) conjecture: Centralizers, Jacobians and spectrally arbitrary sign patterns

DOI10.1016/j.laa.2011.06.051zbMath1244.15020OpenAlexW2079693837WikidataQ123297792 ScholiaQ123297792MaRDI QIDQ417540

Colin Garnett, Bryan L. Shader

Publication date: 14 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.laa.2011.06.051

zbMATH Keywords

Jacobiancharacteristic polynomialcentralizertridiagonal sign pattern

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Sign pattern matrices (15B35)

Related Items (10)

Sign Pattern Matrices ⋮ Bordering for spectrally arbitrary sign patterns ⋮ Counterexamples on spectra of sign patterns ⋮ The nilpotent-centralizer method for spectrally arbitrary patterns ⋮ Zero-nonzero tree patterns that allow Sn∗ ⋮ Inertias of matrices and sign patterns related to a system of second order ODEs ⋮ Algebraic conditions and the sparsity of spectrally arbitrary patterns ⋮ Spectrally arbitrary pattern extensions ⋮ D n,r is not potentially nilpotent for n ⩾ 4r − 2 ⋮ Unnamed Item

Cites Work

• Potentially nilpotent patterns and the nilpotent-Jacobian method
• Some nilpotent, tridiagonal matrices with a special sign pattern
• Allow problems concerning spectral properties of sign pattern matrices: a survey
• Low rank perturbations and the spectrum of a tridiagonal sign pattern.
• Spectrally arbitrary patterns

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