random orthogonal matrix

Hello,

for my work, I have to write a program that gives random orthogonal
matrices, that is that if mu is the Haar measure on O_n(R) and S a
borel set of O_n(R), the probability that my program gives a matrix in
S is mu(X). This is why I wonder if the following algorithm works:

take (v_1,..,v_n) some random vectors in R^n, each coordinate of v_k is
a random number in [-1;+1]. Then, with Gram-Schmidt one can obtain a
sequence of unit orthogonal vectors (w_1,..,w_n). Then the program
returns [w_1,..,w_n].

Does it work ? If yes, is there a better way to do this ? (from the
numerical point of view ..)

thanx in advance,
regards

.

Relevant Pages

  • Re: random orthogonal matrix
    ... Fedor wrote: ... that is that if mu is the Haar measure on O_nand S a ... sequence of unit orthogonal vectors. ...
    (sci.math)
  • Re: random orthogonal matrix
    ... that is that if mu is the Haar measure on ... sequence of unit orthogonal vectors. ... This algorithm is conceptually simple but computationally expensive. ...
    (sci.math)
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