Spectrally arbitrary zero–nonzero patterns of order 4

DOI10.1080/03081080600944829zbMath1112.15015OpenAlexW1995034108MaRDI QIDQ3427136

L. Corpuz, Judith Joanne Mcdonald

Publication date: 14 March 2007

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

Full work available at URL: https://doi.org/10.1080/03081080600944829

zbMATH Keywords

spectrally arbitrarysign patternszero-nonzero patterns

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (22)

Sign Pattern Matrices ⋮ Bordering for spectrally arbitrary sign patterns ⋮ Counterexamples on spectra of sign patterns ⋮ Spectrally arbitrary patterns: Reducibility and the \(2n\) conjecture for \(n = 5\) ⋮ The nilpotent-centralizer method for spectrally arbitrary patterns ⋮ Critical sets of refined inertias for irreducible zero-nonzero patterns of orders 2 and 3 ⋮ New classes of spectrally arbitrary ray patterns ⋮ Spectrally arbitrary ray patterns ⋮ Algebraic conditions and the sparsity of spectrally arbitrary patterns ⋮ Spectrally arbitrary pattern extensions ⋮ Spectrally arbitrary zero-nonzero patterns and field extensions ⋮ Spectrally arbitrary patterns over rings with unity ⋮ On reducible matrix patterns ⋮ Sets of refined inertias of zero-nonzero patterns ⋮ Sparse inertially arbitrary patterns ⋮ Unnamed Item ⋮ Critical sets of inertias for matrix patterns ⋮ Allow problems concerning spectral properties of sign pattern matrices: a survey ⋮ Inertias of zero–nonzero patterns ⋮ The minimum number of nonzeros in a spectrally arbitrary ray pattern ⋮ Complex spectrally arbitrary zero–nonzero patterns ⋮ Spectrally arbitrary patterns over finite fields

Cites Work

• The potentially stable tree sign patterns for dimensions less than five
• Low rank perturbations and the spectrum of a tridiagonal sign pattern.
• Spectrally and inertially arbitrary sign patterns
• Spectrally arbitrary star sign patterns
• Inertially arbitrary (\(2r-1\))-diagonal sign patterns
• On the spectra of close-to-Schwarz matrices
• Potentially nilpotent sign pattern matrices
• Spectrally arbitrary patterns
• Inertially arbitrary patterns
• Minimal Spectrally Arbitrary Sign Patterns
• On the Spectra of Striped Sign Patterns
• Sign pattern matrices that allow a nilpotent matrix
• On the potential stability of star sign pattern matrices
• Symmetric sign pattern matrices that require unique inertia

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