2014/02/26 by Oliver James, James, Oliver, Heung-No Lee +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Information Theory (cs.IT) #Morphological variations and asymmetry #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1402.6757
openalex publication_date 2014/02/26 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28
In this paper, we consider the problem of deriving new eigenvalue\ndistributions of real-valued Wishart matrices that arises in many scientific\nand engineering applications. The distributions are derived using the tools\nfrom the theory of skew symmetric matrices. In particular, we relate the\nmultiple integrals of a determinant, which arises while finding the eigenvalue\ndistributions, in terms of the Pfaffian of skew-symmetric matrices. Pfaffians\nbeing the square root of skew symmetric matrices are easy to compute than the\nconventional distributions that involve Zonal polynomials or beta integrals. We\nshow that the plots of the derived distributions are exactly coinciding with\nthe numerically simulated plots.\n