Extremal sparsity of the companion matrix of a polynomial

DOI10.1016/j.laa.2012.08.017zbMath1269.15007OpenAlexW1985103827MaRDI QIDQ1932635

Xingzhi Zhan, Chao Ma

Publication date: 21 January 2013

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.08.017

zbMATH Keywords

companion matrixpolynomialtranscendence degreesparsityspanning branching

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Factorization of matrices (15A23) Trees (05C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Polynomials in general fields (irreducibility, etc.) (12E05) Matrices, determinants in number theory (11C20)

Related Items (7)

Characterization of a family of generalized companion matrices ⋮ Unnamed Item ⋮ Pentadiagonal companion matrices ⋮ Integrally normalizable matrices and zero-nonzero patterns ⋮ A Class of Quasi-Sparse Companion Pencils ⋮ A note on generalized companion pencils in the monomial basis ⋮ Companion matrix patterns

Cites Work

• Matrix Analysis
• Singular Values of Companion Matrices and Bounds on Zeros of Polynomials
• Minimal Spectrally Arbitrary Sign Patterns
• The inverse of a non-singular free matrix
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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