Orthogonal matrix sampling

[jolyonb]

Ok, I've finally hit the point where I want a special matrix sampler. In this case, I'm after a random orthogonal matrix. I think this can be done in the following way:

1. Specify number of dimensions (n)
2. Sample n random vectors of this dimension
3. Normalize the first vector
4. Take the second vector, subtract off the components in the direction of the first vector, and then normalize it
5. Repeat with the third, subtracting off components in the direction of the first two vectors etc
6. Put the resulting n orthonormal vectors in a matrix

[ChristopherChudzicki]

So, sample a generic n by n matrix, then do Gramm-Schmidt on the rows (or columns)?

That sounds like a good approach. This would work for unitary matrices, too, right? Just sample the original vectors over C instead of R.

[jolyonb]

Basically. Unitary will work the same way.