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In order to generate a random orthogonal matrix distributed according to Haar measure over the orthogonal group it is natural to start with a matrix of normal random variables and then factor it by the singular value decomposition. A more efficient method is obtained by using Householder transformations. We propose another alternative based on the product of {n (n - 1) /2} orthogonal matrices, each of which represents an angle of rotation. Some numerical comparisons of alternative methods are made.
Anderson et al. (Wed,) studied this question.
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