Applications of an inequality in information theory to matrices

Bapat, R. B. (1986) Applications of an inequality in information theory to matrices Linear Algebra and its Applications, 78 . pp. 107-117. 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(86)90018-2

Abstract

If x and y are nonnegative vectors of order n, and if Σni=1xi=Σni=1yi, then a well-known inequality asserts that ∏ni=1xxii≥∏ni=1yxii , with equality if and only if x = y. In this paper various situations are considered where this inequality can be applied to obtain inequalities concerning nonnegative matrices. In particular, inequalities are proved concerning nonnegative matrices which are diagonally equivalent, permanents and functions more general than the permanent, and diagonal products and circuit products of nonnegative matrices.

Item Type:Article
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ID Code:78316
Deposited On:19 Jan 2012 06:30
Last Modified:19 Jan 2012 06:30

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