An inverse eigenvalue problem for structured matrices determined by graph pairs

DOI10.1016/j.laa.2024.07.007MaRDI QIDQ6615438

Adam H. Berliner, Sooyeong Kim, Pauline van den Driessche, Michael S. Cavers, Minerva Catral

Publication date: 8 October 2024

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

zbMATH Keywords

graphdigraphinverse eigenvalue problemstructured matrix

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Inverse problems in linear algebra (15A29) Eulerian and Hamiltonian graphs (05C45) Toeplitz, Cauchy, and related matrices (15B05)

Cites Work

• Construction of matrices with a given graph and prescribed interlaced spectral data
• Spectrally arbitrary patterns: Reducibility and the \(2n\) conjecture for \(n = 5\)
• Spectrally arbitrary patterns
• The bifurcation lemma for strong properties in the inverse eigenvalue problem of a graph
• Stability of sign patterns from a system of second order ODEs
• Generalizations of the strong Arnold property and the minimum number of distinct eigenvalues of a graph
• Inertias of matrices and sign patterns related to a system of second order ODEs
• The Quadratic Eigenvalue Problem
• Inverse Problems and Zero Forcing for Graphs
• Techniques for identifying inertially arbitrary patterns

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