# Resolution of the Symmetric Nonnegative Inverse Eigenvalue Problem for Matrices Subordinate to a Bipartite Graph

Resolution of the Symmetric Nonnegative Inverse Eigenvalue Problem for Matrices Subordinate to a... There is a symmetric nonnegative matrix A, subordinate to a given bipartite graph G on n vertices, with eigenvalues λ1≥λ2≥≥λ n if and only if, λ1 + λ n ≥0, λ2 + λ n-1≥0,...,λ m + λ n - m + 1≥0, λ m + 1≥0,...,λ n - m ≥0, in which m is the matching numberof G. Other observations are also made about the symmetric nonnegative inverse eigenvalue problem with respect to a graph http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Resolution of the Symmetric Nonnegative Inverse Eigenvalue Problem for Matrices Subordinate to a Bipartite Graph

, Volume 8 (2) – Oct 19, 2004
5 pages

/lp/springer_journal/resolution-of-the-symmetric-nonnegative-inverse-eigenvalue-problem-for-GCPxuwbfEm
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/B:POST.0000042733.60148.47
Publisher site
See Article on Publisher Site

### Abstract

There is a symmetric nonnegative matrix A, subordinate to a given bipartite graph G on n vertices, with eigenvalues λ1≥λ2≥≥λ n if and only if, λ1 + λ n ≥0, λ2 + λ n-1≥0,...,λ m + λ n - m + 1≥0, λ m + 1≥0,...,λ n - m ≥0, in which m is the matching numberof G. Other observations are also made about the symmetric nonnegative inverse eigenvalue problem with respect to a graph

### Journal

PositivitySpringer Journals

Published: Oct 19, 2004

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