A comparison of some bounds for the nontrivial eigenvalues of stochastic matrices
β Scribed by Christoph Zenger
- Publisher
- Springer-Verlag
- Year
- 1972
- Tongue
- English
- Weight
- 92 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0029-599X
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π SIMILAR VOLUMES
## Abstract Eigenvalue bounds are provided. It is proved that the minimal eigenvalue of a __Z__βmatrix strictly diagonally dominant with positive diagonals lies between the minimal and the maximal row sums. A similar upper bound does not hold for the minimal eigenvalue of a matrix strictly diagonal
We give a lower bound for the second smallest eigenvalue of Laplacian matrices in terms of the isoperimetric number of weighted graphs. This is used to obtain an upper bound for the real parts of the nonmaximal eigenvalues of irreducible nonnegative matrices.