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I am wondering how to randomly and uniformly generate a hyperplane (passing through the origin) in R^m

I am new to this concept and couldn't find an explanation that it's easy to understand for a beginner .

Ree GH
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The easiest way to get a random hyperplane is just to generate a random vector V, and then take your hyperplane as all points P such that P \dot V = 0.

The distribution you choose for your random vectors needs to be rotationally symmetric. I think the simplest way to do that for arbitrary dimension is to generate an independent Gaussian-distributed coordinate for each axis.

Matt Timmermans
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  • Related question: [random unit vector in multi-dimensional space](https://stackoverflow.com/questions/6283080/random-unit-vector-in-multi-dimensional-space). The accepted answer uses independent Gaussian coordinates. Another answer remarks there is [boost/random/uniform_on_sphere](https://www.boost.org/doc/libs/1_47_0/boost/random/uniform_on_sphere.hpp) for C++. Also, https://stackoverflow.com/search?q=random+point+on+sphere returns lots of results. – Stef Apr 28 '22 at 08:34