We give bounds for the second real eigenvalue of nonegative matrices and Z-matrices. Furthermore, we establish upper bounds for the maximal spectral radii of principal submatrices of nonnegative matrices. Using these bounds, we prove that our inequality for the second real eigenvalue of the adjacenc
On the second eigenvalue of matrices associated with TCP
β Scribed by Abraham Berman; Thomas Laffey; Arie Leizarowitz; Robert Shorten
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 120 KB
- Volume
- 416
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
Let (P , , β§) be a locally finite meet semilattice. Let S = {x 1 , x 2 , . . . , x n }, x i x j β i j, be a finite subset of P and let f be a complex-valued function on P . Then the n Γ n matrix (S) f , where is called the meet matrix on S with respect to f . The join matrix on S with respect to f
We consider matrices containing two diagonal bands of positive entries. We show that all eigenvalues of such matrices are of the form rΞΆ , where r is a nonnegative real number and ΞΆ is a pth root of unity, where p is the period of the matrix, which is computed from the distance between the bands. We
Nilli, A., On the second eigenvalue of a graph, Discrete Mathematics 91 (1991) 207-210. It is shown that the second largest eigenvalue of the adjacency matrix of any G containing two edges the distance between which is at least 2k + 2 is at least (2G -l)/(k + 1).