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I want to implement the method of sampling (uniformly) points on Stiefel manifold but I'm failing to find any kind of research/article/work that can give some info about the methods and techniques of doing it.

I found an old paper, but it is really hard to follow (no background info is given, and overall it is not very accessible).

Is there any work that can help me to tackle the problem? I would be really grateful if you could share anything.

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A simple method of generating such samples is as follows. Draw $n m$ random samples from $N(0,1)$ and arrange them into an $n\times m$ matrix $X$. Then $X(X^{\top}X)^{-1/2}$ is a random matrix that follows the uniform distribution on the Stiefel manifold $V_m(\mathbb{R}^n)$ (e.g., Theorem 2.2.1 in Chikuse, Y. (2003). Statistics on Special Manifolds).

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