Create random matrix with orthonormal columns?

Question

In Julia, is there any function or way to generate a random matrix with orthonormal columns of arbitrary dimensions (not necessarily square, could be rectangular/tall matrix)?

what do you mean by a random matrix? What distribution do you want? — Oscar Smith, Aug 15 '22 at 20:55
I guess James means this: https://stackoverflow.com/questions/38426349/how-to-create-random-orthonormal-matrix-in-python-numpy seems one way is to call SciPy via PyCall.jl — Przemyslaw Szufel, Aug 15 '22 at 21:15
You can read https://nhigham.com/2020/04/22/what-is-a-random-orthogonal-matrix/ — Picaud Vincent, Aug 16 '22 at 21:54

score 4 · Accepted Answer · answered Aug 15 '22 at 22:32

Since the columns of Q in a QR decomposition are orthonormal, I think you could just perform a QR decomposition on a random matrix.

julia> using LinearAlgebra

julia> qr(rand(5)).Q
5×5 LinearAlgebra.QRCompactWYQ{Float64, Matrix{Float64}, Matrix{Float64}}:
 -0.418858  -0.339672   -0.113064   -0.664132   -0.505298
 -0.339672   0.918683   -0.0270673  -0.158992   -0.120967
 -0.113064  -0.0270673   0.99099    -0.0529223  -0.0402654
 -0.664132  -0.158992   -0.0529223   0.689136   -0.236517
 -0.505298  -0.120967   -0.0402654  -0.236517    0.820048

If you don't need all 5 columns, you can just take the first k that you need.

Create random matrix with orthonormal columns?

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