Condition numbers of indefinite rank 2 ghost Wishart matrices
Author(s)Movassagh, Ramis; Edelman, Alan
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Abstract We define an indefinite Wishart matrix as a matrix of the form A= W[superscript T]WΣ, where Σ is an indefinite diagonal matrix and W is a matrix of independent standard normals. We focus on the case where W is L×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 < ∞. We then corroborate our work by comparing them against numerical experiments.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Linear Algebra and its Applications
Movassagh, Ramis, and Alan Edelman. “Condition Numbers of Indefinite Rank 2 Ghost Wishart Matrices.” Linear Algebra and Its Applications, vol. 483, Oct. 2015, pp. 342–51.
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