Explicit Isomorphism between $O(3,3)$ and $GL(4, \mathbb{R})$

Question

I have seen it stated that $O(3,3) \cong GL(4, \mathbb{R})$, but I have never seen the isomorphism explicitly defined. Does anyone know what the isomorphism is or where I might be able to find it?

Any insight is appreciated!

Answer 1

That can not be right: the dimension of the orthogonal groups in $m$ dimensions is $\frac{1}{2}m(m-1)$, which implies that $O(3, 3)$ is $15$-dimensional. $GL(4, \mathbb{R})$ on the other hand is $16$-dimensional.