Undirected graphs of Hermitian matrices that admit only two distinct eigenvalues

DOI10.1016/j.laa.2014.02.022zbMath1295.05141OpenAlexW1975206272MaRDI QIDQ2250939

Charles R. Johnson, Zhao Chen, Matthew Grimm, Paul R. McMichael

Publication date: 22 July 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2014.02.022

zbMATH Keywords

graphsHermitian matrixinner product spacesHermitian projectioneigenvalue multiplicitiesdual multiplicity graphs

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Quadratic and bilinear forms, inner products (15A63)

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Cites Work

• Linearly independent vertices and minimum semidefinite rank
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• On the Minimum Rank Among Positive Semidefinite Matrices with a Given Graph
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
• The Parter--Wiener Theorem: Refinement and Generalization
• On the minimum number of distinct eigenvalues for a symmetric matrix whose graph is a given tree