title: The exact distribution of the condition number of complex random matrices.
abstract: 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 λ1 > λ2 > …>λn > 0 and σ1 > σ2 > …>σn > 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 k2(G(m×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.
authors.affiliation: School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.
authors.forename: Lin
authors.initials: L
authors.lastname: Shi
authors.affiliation: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.
authors.forename: Taibin
authors.initials: T
authors.lastname: Gan
authors.affiliation: School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.
authors.forename: Hong
authors.initials: H
authors.lastname: Zhu
authors.affiliation: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.
authors.forename: Xianming
authors.initials: X
authors.lastname: Gu
mesh_terms: D000465:Algorithms; D008433:Mathematics; D009716:Numerical Analysis, Computer-Assisted