Lower bounds for matrices
β Scribed by Grahame Bennett
- Book ID
- 107825098
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 843 KB
- Volume
- 82
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
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.
Let A = (a n,k ) n,k 0 be a non-negative matrix. Denote by L p,q (A) the supremum of those L satisfying AX q L X p (X β p , X 0), and define L (p),q (A) = L p,q (A) (p > 0). We derive a range for the value of L p,q (A NM W ), where 0 < q p < 1 and A NM W denotes the NΓΆrlund matrix associated with th