Matrices totally positive relative to a tree, II
Copyright policy )Matrices totally positive relative to a tree, II
In this paper we prove that for a general tree $T$, if $A$ is T-TP, all the submatrices of $A$ associated with the deletion of pendant vertices are $P$-matrices, and $\det A>0$, then the smallest eigenvalue has an eigenvector signed according to $T$.
11 pages, 2 figures, submitted to LAA
- William & Mary United States
- Universidad Loyola Andalucía Spain
- University of Alcalá Spain
Eigenvalues, singular values, and eigenvectors, Graphs and linear algebra (matrices, eigenvalues, etc.), Totally positive matrix, Matemáticas, Totally positive relative to a tree, spectral theory, Sylvester’s identity, graph, 15A18, 94C15, Graph, totally positive relative to a tree, Positive matrices and their generalizations; cones of matrices, Sylvester's identity, Neumaier conclusion, totally positive matrix, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Spectral theory
Eigenvalues, singular values, and eigenvectors, Graphs and linear algebra (matrices, eigenvalues, etc.), Totally positive matrix, Matemáticas, Totally positive relative to a tree, spectral theory, Sylvester’s identity, graph, 15A18, 94C15, Graph, totally positive relative to a tree, Positive matrices and their generalizations; cones of matrices, Sylvester's identity, Neumaier conclusion, totally positive matrix, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Spectral theory
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