Singular random matrix decompositions: Jacobians

DOI10.1016/j.jmva.2004.03.002zbMath1097.15018OpenAlexW2029712917MaRDI QIDQ1776872

José A. Díaz-García, Graciela M. González-Farías

Publication date: 12 May 2005

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2004.03.002

zbMATH Keywords

random matricesHausdorff measurespectral decompositionCholesky decompositionsQR factorizationsingular distribution\(L'U\) factorizationpolar singular value decompositionsymmetric nonnegative definite square root decomposition

Mathematics Subject Classification ID

Factorization of matrices (15A23) Random matrices (algebraic aspects) (15B52) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (15)

Functions of singular random matrices with applications ⋮ A note about measures and Jacobians of singular random matrices ⋮ Inverse Wishart distributions based on singular elliptically contoured distributions ⋮ The Jacobians of matrix transformation about singular random matrices and its applications ⋮ A note about measures, Jacobians and Moore-Penrose inverse ⋮ Singular matrix variate Birnbaum-Saunders distribution under elliptical models ⋮ Spherical ensembles ⋮ On generalized multivariate analysis of variance ⋮ The distribution of residuals from a general elliptical linear model ⋮ On the marginal distribution of the diagonal blocks in a blocked Wishart random matrix ⋮ Singular matrix variate beta distribution ⋮ The distribution of the residual from a general elliptical multivariate linear model ⋮ Singular extended skew-elliptical distributions ⋮ Predictive inference for singular multivariate elliptically contoured distributions ⋮ On the Jacobians of singular matrix decomposition and its application

Cites Work

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• On singular Wishart and singular multivariate beta distributions
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• Proof of the conjectures of H. Uhlig on the singular multivariate beta and the Jacobian of a certain matrix transformation
• Singular Wishart and multivariate beta distributions
• Multivariate calculation. Use of the continuous groups
• Vec and vech operators for matrices, with some uses in jacobians and multivariate statistics
• Multivariate Beta Distributions and Independence Properties of the Wishart Distribution
• Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
• Normal Multivariate Analysis and the Orthogonal Group
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