✦ LIBER ✦

A Note on von Neumann's Trace Inequalitv

✍ Scribed by Rolf Dieter Grigorieff

Publisher: John Wiley and Sons
Year: 1991
Tongue: English
Weight: 106 KB
Volume: 151
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19911510122

No coin nor oath required. For personal study only.

✦ Synopsis

The following trace inequality first proved by VON NEUMA" [6] has found repeated interest in the literature:

Theorem. Lel A , B be complex n x n mntriceu. Then (*I Itr ( W I 5 (44, a m ) where a(A) = (al, a, , . . ., a, ) denotes the ordered vector of singular values a1 2 u2 2 2 an of A and ( a , a ) the euclideun scalar product.

The importance of this result stems from the fact that it is used as an essential tool in SCHATTEN'S theory of cross-spaces and more recently in BALL'S treatment of the equations of nonlinear elasticity.

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