Eigenvalues and Condition Numbers of Complex Random Matrices

DOI10.1137/S089547980342204XzbMath1086.15025OpenAlexW1975494153MaRDI QIDQ4651004

Mayer Alvo, Tharmalingam Ratnarajah, Rémi Vaillancourt

Publication date: 21 February 2005

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s089547980342204x

zbMATH Keywords

eigenvalue distributionGaussian random matricescomplex random matrixcomplex Wishart matrixcomplex hypergeometric functionscomplex zonal polynomialscondition number distribution

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Probability distributions: general theory (60E05) Random matrices (algebraic aspects) (15B52) Conditioning of matrices (15A12)

Related Items (18)

Generalized heterogeneous hypergeometric functions and the distribution of the largest eigenvalue of an elliptical Wishart matrix ⋮ Weighted Condition Number Distributions Emanating from Complex Noncentral Wishart Type Matrices ⋮ Eigenvalue distributions of beta-Wishart matrices ⋮ The Jacobians of matrix transformation about singular random matrices and its applications ⋮ Zonal Polynomials and Hypergeometric Functions of Quaternion Matrix Argument ⋮ Algorithm for the product of Jack polynomials and its application to the sphericity test ⋮ Asymptotic behavior of the distributions of eigenvalues for beta-Wishart ensemble under the dispersed population eigenvalues ⋮ Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions ⋮ Extreme eigenvalue distributions of some complex correlated non-central Wishart and gamma-Wishart random matrices ⋮ Spherical ensembles ⋮ Roy's largest root under rank-one perturbations: the complex valued case and applications ⋮ Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix ⋮ The Density Functions of the Singular Quaternion Normal Matrix and the Singular Quaternion Wishart Matrix ⋮ Queues, stores, and tableaux ⋮ On the Jacobians of singular matrix decomposition and its application ⋮ Complex bimatrix variate generalised beta distributions ⋮ Complex random matrices and Rician channel capacity ⋮ Complex singular Wishart matrices and applications

Uses Software

• Mathematica

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