Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (5): 1323-1327.
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LIU Xiu-Sheng
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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/m∑mi=1r i2m)1/2. In particular, |dχ(A)|2≤1/m∑mi=1ri2m.
Key words: Singular-values, Symmetry class of tensors, Induced operator
CLC Number:
LIU Xiu-Sheng. Inequalities for Generalized Matrix Functions[J].Acta mathematica scientia,Series A, 2011, 31(5): 1323-1327.
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[1] Marcus M, Minc H. Generalized matrix functions. Trans Amer Math Soc, 1965, 116: 316--329 [2] Marcus M. Finite Dimensional Multilinear Algebra, Part 1. New York: Marcle Dekker, 1973 [3] Johnson C R, Zhang F. An operator inequality and matrix normality. Linear Algebra and Appl, 1996, 240: 105--110 [4] Liu X S. Inequalities on the variation for general matrix function. Acta Math Scientia, 2004, 24A: 626--631 [5] Li C K, Zahara A. Induced operators on symmetry classes of tensors. Trans Amer Math Soc, 2002, 345: 807--836
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