Let $O(1,n)$ be the orthogonal group of the quadratic form $b(x)=-x_0^2+\sum\limits_{i=1}^n x_i^2$. In other words, $$O(1,n)=\{T\in GL(n+1,\Bbb{R}|b(Tx)=b(x),\forall x\in R^{n+1}\}$$ Elements in $O(1,n)$ will be written in the block form with respect to the natural basis of $\Bbb{R}^{n+1}$. The standard basis $\{e_i\}_0^n$ corresponds to block matrices of the form $\begin{pmatrix}1\times 1 & 1\times n \\n\times 1 & n\times n \end{pmatrix}$
What is this "standard basis" $\{e_i\}_0^n$ that is referred to here? $O(1,n)$ is clearly not a vector space. So does $\{e_i\}_0^n$ generate the whole of $O(1,n)$ as a group?