Inequalities for mixed Schur functions

Bapat, R. B. (1986) Inequalities for mixed Schur functions Linear Algebra and its Applications, 83 . pp. 143-149. ISSN 0024-3795

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If Ak =(akij), k=1,2,...,n, are n×n positive semidefinite matrices and if α:SnC, where Sn is the symmetric group of degree n, an inequality is obtained for the "mixed Schur function," R When the matrices Ak, k=1,2,...,n, are all equal, we get some known results due to Schur as consequences of the inequality. It is also deduced that the mixed discriminant of a set of positive semidefinite matrices exceeds or equals the geometric mean of their determinants.

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