Bapat, R. B. (1987) Two inequalities for the Perron Root Linear Algebra and its Applications, 85 . pp. 241-248. ISSN 0024-3795
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Official URL: http://www.sciencedirect.com/science/article/pii/0...
Related URL: http://dx.doi.org/10.1016/0024-3795(87)90220-5
Abstract
If A, B are irreducible, nonnegative n×n matrices with a common right eigenvector and a common left eigenvector corresponding to their respective spectral radii r(A), r(B), then it is shown that for any t∈[0, 1], r(tA+(1-t)Bt)≥tr(A)+ (1-t)r(B), where Bt is the transpose of B. Another inequality is proved that involves r(A) and r(∑lDlAEI), where A is a nonnegative, irreducible matrix and DI, EI are positive definite diagonal matrices. These inequalities generalize previous results due to Levinger and due to Friedland and Karlin.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| ID Code: | 77910 |
| Deposited On: | 14 Jan 2012 15:42 |
| Last Modified: | 14 Jan 2012 15:42 |
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