Bapat, R. B. ; Sunder, V. S.
(1986)
*An extremal property of the permanent and the determinant*
Linear Algebra and its Applications, 76
.
pp. 153-163.
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)90220-X

## Abstract

Given an n×n matrix A, define the n!×n! matrix Ã, with rows and columns indexed by the permutation group S_{n}, with (σ,τ) entry Π^{n}_{i=1} a _{τ(i), σ(i)}. It is shown that if A is positive semidefinite, then det A is the smallest eigenvalue of Ã; it is conjectured that per A is the largest eigenvalue of Ã, and the conjecture proved for n^{≤}3. Several known and some unknown inequalities are derived as consequences.

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Deposited On: | 09 Aug 2011 11:47 |

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