Condition numbers of indefinite rank 2 ghost Wishart matrices
Name
Edelman_Condition numbers.pdf
Size
277 KB
Format
Adobe PDF
Checksum (MD5)
e18544e32f7f1e6744f08d339f334f51
Author(s)
Movassagh, Ramis
Edelman, Alan
Date Issued
October 2015
Journal
Linear Algebra and its Applications
Publisher
Elsevier BV
Citation
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.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.LAA.2015.05.027
