Two inequalities for the Perron Root

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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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.

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Deposited On:14 Jan 2012 15:42
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