The Perron-Frobenius theorem without additivity
✍ Scribed by Elon Kohlberg
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 233 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0304-4068
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
If A is an n x n nonnegative, irreducible matrix, then there exists /L(A) > 0. and a positive vector x such that max,a,,x, = &4)x,. i = 1,2. n. Furthermore, ,n(A) is the maximum geometric mean of a circuit in the weighted directed graph corresponding to A. This theorem, which we refer to as the max
We prove discrete versions of nodal domain theorems; in particular, an eigenvector corresponding to the sth smallest eigenvalue of a graph Laplacian has at most s nodal domains. We compare our results to those of Courant and Pleijel on nodal domains of continuous Laplacians, and to those of Fiedler