The Exact Distribution of the Condition Number of Complex Random Matrices
نویسندگان
چکیده
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.
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عنوان ژورنال:
دوره 2013 شماره
صفحات -
تاریخ انتشار 2013