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.
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G. W. Stewart (1980) studied this question.
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