Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (5): 1323-1327.

• Articles • Previous Articles     Next Articles

Inequalities for Generalized Matrix Functions

 LIU Xiu-Sheng   

  1. Department of Mathematics and Physics, Huangshi Institute of Technology, Hubei |Huangshi 435003
  • Received:2009-08-23 Revised:2010-09-02 Online:2011-10-25 Published:2011-10-25

Abstract:

Let Sm denote the symmetric group of degree m and G be a subgroup of Sm. Let χ be a character of degree 1 on G . Suppose A is an m-by-m matrix complex matrix with singular-values r1, r2,…, rm. Denote dχ(A)=∑σ∈G χ(σ)∏i=1ma1,σ(i). It is proved that

|dχ(A)|≤(1/mmi=1r i2m)1/2.

In particular,
|dχ(A)|2≤1/mmi=1ri2m.

Key words: Singular-values, Symmetry class of tensors, Induced operator

CLC Number: 

  • 15A45
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