The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators

1980/06/01 by G. W. Stewart · 4 citations
Mathematics · Computer Science · #Random Matrices and Applications #Bayesian Methods and Mixture Models #Point processes and geometric inequalities #Mathematics #Orthogonal matrix #Random matrix #Estimator #Orthogonal array #Applied mathematics #Random variate #Matrix (chemical analysis) #Circular law #Group (periodic table) #Random variable #Multivariate random variable #Orthogonal basis #Statistics #Eigenvalues and eigenvectors #Taguchi methods

paper · doi:10.1137/0717034

openalex publication_date 1980/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/06

Abstract

This paper presents a method for generating pseudo-random orthogonal matrices from the Haar distribution for the group of orthogonal matrices. The random matrices are expressed as products of n - 1 Householder transformations, which can be computed in O(n² ) time. The technique is used in an empirical study of two methods for estimating the condition number of a matrix.

Cited by

• The Subgroup Algorithm for Generating Uniform Random Variables
• Generating Uniform Incremental Grids on SO (3) Using the Hopf Fibration
• Random matrix theory
• Orthogonal matrix [wikipedia]