Condition Numbers of Indefinite Rank 2 Ghost Wishart Matrices
arXiv:1207.3062 · doi:10.1016/j.laa.2015.05.027
Abstract
We define an indefinite Wishart matrix as a matrix of the form A=W^{T}WΣ, where Σis an indefinite diagonal matrix and W is a matrix of independent standard normals. We focus on the case where W is L by 2 which has engineering applications. We obtain the distribution of the ratio of the eigenvalues of A. This distribution can be "folded" to give the distribution of the condition number. We calculate formulas for W real (β=1), complex (β=2), quaternionic (β=4) or any ghost 0<β<\infty. We then corroborate our work by comparing them against numerical experiments.
10 pages, 13 figures