The Exact Distribution of the Condition Number of Complex Random Matrices

Let G (m×n) (m ≥ n) be a complex random matrix and W = G (m×n) (H) G (m×n) which is the complex Wishart matrix. Let λ (1) > λ (2) > …>λ (n) > 0 and σ (1) > σ (2) > …>σ (n) > 0 denote the eigenvalues of the W and singular values of G (m×n), respectively. The 2-norm condition n...

Descripción completa

Detalles Bibliográficos
Autores principales: Shi, Lin, Gan, Taibin, Zhu, Hong, Gu, Xianming
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2013
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3859023/
https://www.ncbi.nlm.nih.gov/pubmed/24376385
http://dx.doi.org/10.1155/2013/729839
_version_ 1782295364350509056
author Shi, Lin
Gan, Taibin
Zhu, Hong
Gu, Xianming
author_facet Shi, Lin
Gan, Taibin
Zhu, Hong
Gu, Xianming
author_sort Shi, Lin
collection PubMed
description Let G (m×n) (m ≥ n) be a complex random matrix and W = G (m×n) (H) G (m×n) which is the complex Wishart matrix. Let λ (1) > λ (2) > …>λ (n) > 0 and σ (1) > σ (2) > …>σ (n) > 0 denote the eigenvalues of the W and singular values of G (m×n), respectively. The 2-norm condition number of G (m×n) is [Formula: see text]. In this paper, the exact distribution of the condition number of the complex Wishart matrices is derived. The distribution is expressed in terms of complex zonal polynomials.
format Online
Article
Text
id pubmed-3859023
institution National Center for Biotechnology Information
language English
publishDate 2013
publisher Hindawi Publishing Corporation
record_format MEDLINE/PubMed
spelling pubmed-38590232013-12-29 The Exact Distribution of the Condition Number of Complex Random Matrices Shi, Lin Gan, Taibin Zhu, Hong Gu, Xianming ScientificWorldJournal Research Article Let G (m×n) (m ≥ n) be a complex random matrix and W = G (m×n) (H) G (m×n) which is the complex Wishart matrix. Let λ (1) > λ (2) > …>λ (n) > 0 and σ (1) > σ (2) > …>σ (n) > 0 denote the eigenvalues of the W and singular values of G (m×n), respectively. The 2-norm condition number of G (m×n) is [Formula: see text]. In this paper, the exact distribution of the condition number of the complex Wishart matrices is derived. The distribution is expressed in terms of complex zonal polynomials. Hindawi Publishing Corporation 2013-11-25 /pmc/articles/PMC3859023/ /pubmed/24376385 http://dx.doi.org/10.1155/2013/729839 Text en Copyright © 2013 Lin Shi et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Shi, Lin
Gan, Taibin
Zhu, Hong
Gu, Xianming
The Exact Distribution of the Condition Number of Complex Random Matrices
title The Exact Distribution of the Condition Number of Complex Random Matrices
title_full The Exact Distribution of the Condition Number of Complex Random Matrices
title_fullStr The Exact Distribution of the Condition Number of Complex Random Matrices
title_full_unstemmed The Exact Distribution of the Condition Number of Complex Random Matrices
title_short The Exact Distribution of the Condition Number of Complex Random Matrices
title_sort exact distribution of the condition number of complex random matrices
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3859023/
https://www.ncbi.nlm.nih.gov/pubmed/24376385
http://dx.doi.org/10.1155/2013/729839
work_keys_str_mv AT shilin theexactdistributionoftheconditionnumberofcomplexrandommatrices
AT gantaibin theexactdistributionoftheconditionnumberofcomplexrandommatrices
AT zhuhong theexactdistributionoftheconditionnumberofcomplexrandommatrices
AT guxianming theexactdistributionoftheconditionnumberofcomplexrandommatrices
AT shilin exactdistributionoftheconditionnumberofcomplexrandommatrices
AT gantaibin exactdistributionoftheconditionnumberofcomplexrandommatrices
AT zhuhong exactdistributionoftheconditionnumberofcomplexrandommatrices
AT guxianming exactdistributionoftheconditionnumberofcomplexrandommatrices

Ejemplares similares