We consider the asymptotic behaviour of the smallest singular values of the n x N sections of a general infinite Cauchy-Toeplitz matrix.
Notes on Hilbert and Cauchy matrices
✍ Scribed by Miroslav Fiedler
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 109 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
✦ Synopsis
Inspired by examples of small Hilbert matrices, the author proves a property of symmetric totally positive Cauchy matrices, called AT-property, and consequences for the Hilbert matrix.
📜 SIMILAR VOLUMES
## Abstract We determine bounds for the spectral and 𝓁~__p__~ norm of Cauchy–Hankel matrices of the form __H__~__n__~=[1/(__g__+__h__(__i__+__j__))]^__n__^~__i,j__=1~≡ ([1/(__g__+__kh__)]^__n__^~__i,j__=1~), __k__=0, 1,…, __n__ –1, where __k__ is defined by __i__+__j__=__k__ (mod __n__). Copyright
The so-called Generalized-Confluent Cauchy-Vandermonde (GCCV) matrices of the form [C,V] consisting of a generalized-confluent Cauchy part C and a generalized-confluent Vandermonde part V are considered. A simple relationship between GCCV and classical confluent Cauchy-Vandermonde (CCV) matrices is
We note certain properties of the Hilbert-Kunz function and Hilbert-Kunz multiplicity, including a strengthened inequality between Hilbert-Kunz and Hilbert-Samuel multiplicities and a characterization of a mixed Hilbert function incorporating both ordinary and Frobenius powers of ideals.