A new type of lower bound for the largest eigenvalue of a symmetric matrix
โ Scribed by Piet Van Mieghem
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 162 KB
- Volume
- 427
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
Let A be a positive definite, symmetric matrix. We wish to determine the largest eigenvalue, 1,. We consider the power method, i.e. that of choosing a vector v. and setting vk = Akvo; then the Rayleigh quotients Rk = (Auk, vk)/( ok, ok) usually converge to 21 as k -+ 03 (here (u, v) denotes their in
are encountered in many systems and control applications, and these matrix equations contain several linear matrix equations as special cases. In the present work, we introduce the inequalities for the determinant of the solutions of these matrix equations, separately. Then using these inequalities,
We first give a result on eigenvalues of the line graph of a graph. We then use the result to present a new upper bound for eigenvalues of the Laplacian matrix of a graph. Moreover we determine all graphs the largest eigenvalue of whose Laplacian matrix reaches the upper bound.