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Applications of an inequality in information theory to matrices

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
78
Identifiers
DOI: 10.1016/0024-3795(86)90018-2

Abstract

Abstract If x and y are nonnegative vectors of order n, and if Σ n i = 1 x i = Σ n i = 1 y i , then a well-known inequality asserts that Π n i = 1 x x i i ⩾ Π n i = 1 y x i i , 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.

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