The Exact Distribution of the Condition Number of Complex Random Matrices
Let Gm×n (m≥n) be a complex random matrix and W=Gm×nHGm×n which is the complex Wishart matrix. Let λ1>λ2>…>λn>0 and σ1>σ2>…>σn>0 denote the eigenvalues of the W and singular values of Gm×n, respectively. The 2-norm condition number of Gm×n is κ2Gm×n=λ1/λn=σ1/σn. In this paper...
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/729839 |
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| author | Lin Shi Taibin Gan Hong Zhu Xianming Gu |
| author_facet | Lin Shi Taibin Gan Hong Zhu Xianming Gu |
| author_sort | Lin Shi |
| collection | DOAJ |
| description | Let Gm×n (m≥n) be a complex random matrix and W=Gm×nHGm×n which is the complex Wishart matrix. Let λ1>λ2>…>λn>0 and σ1>σ2>…>σn>0 denote the eigenvalues of the W and singular values of Gm×n, respectively. The 2-norm condition number of Gm×n is κ2Gm×n=λ1/λn=σ1/σn. 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 | Article |
| id | doaj-art-782d9785bc7d4e6b94544caa6ccb83ce |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-782d9785bc7d4e6b94544caa6ccb83ce2025-02-03T01:27:37ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/729839729839The Exact Distribution of the Condition Number of Complex Random MatricesLin Shi0Taibin Gan1Hong Zhu2Xianming Gu3School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaLet Gm×n (m≥n) be a complex random matrix and W=Gm×nHGm×n which is the complex Wishart matrix. Let λ1>λ2>…>λn>0 and σ1>σ2>…>σn>0 denote the eigenvalues of the W and singular values of Gm×n, respectively. The 2-norm condition number of Gm×n is κ2Gm×n=λ1/λn=σ1/σn. 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.http://dx.doi.org/10.1155/2013/729839 |
| spellingShingle | Lin Shi Taibin Gan Hong Zhu Xianming Gu The Exact Distribution of the Condition Number of Complex Random Matrices The Scientific World Journal |
| 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 |
| url | http://dx.doi.org/10.1155/2013/729839 |
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