Re: random orthogonal matrix

Fedor wrote:
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


It won't work, but if you pick your v_k to be Gaussian random variables it will work.
.

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