SCHINDLER, W (1995) BI-INVARIANT INTEGRALS ON GL(N) WITH APPLICATIONS. MATHEMATISCHE NACHRICHTEN, 173. pp. 297-320. ISSN 0025-584X,
Full text not available from this repository.Abstract
In this paper measures and functions on GL(n) are called bi-invariant if they are invariant under left and right multiplication of their arguments. If v is any bi-invariant Borel measure on GL(n), then there exists a unique Borel measure v* on D-+greater than or equal to(n), the set of all diagonal matrices of rank n with positive non-increasing diagonal entries, such that [GRAPHICS] holds for each v-integrable bi-invariant function f:GL(n) --> R. An explicit formula for v* will be derived in case v equals the Lebesgue measure on GL(n) and the above integral formula will be applied to concrete integration problems. In particular, if v is a probability measure, then v* can be interpreted as the distribution of the singular value vector. This fact will be used to derive a stochastic version of a theorem from perturbation theory concerning the numerical computation of the polar decomposition.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | POLAR DECOMPOSITION; |
| Depositing User: | Dr. Gernot Deinzer |
| Last Modified: | 19 Oct 2022 08:38 |
| URI: | https://pred.uni-regensburg.de/id/eprint/52871 |
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