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5 votes
4 answers
3k views

Parametrization of O(3)

Is there a simple way to parametrize the orthogonal group O(3) of 3 by 3 orthogonal matrices?
0 votes
2 answers
1k views

Is it possible to obtain the vectors orthogonal to a given one by orthogonal transformations?

Hello, everyone! Supposing that there is a unit vector in $n$-dimensional real space $\mathbf{x}_1\in\mathbb{R}^n$, I want to get a group of $n-1$ vectors to form an orthogonal basis with $\mathbf{x}...

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