Define a Pseudo-Riemannian Metric $g$ in $\mathbb{R}^{n+1}$ by $g(u,v)=-u_0v_0+u_1v_1+...+u_nv_n$, where $u=(u_0,u_1,...u_n)$. Let $\eta\in\mathbb{R}^{n+1}$ be a vector such that $g(\eta,\eta)=-1$. Is it possible to find a basis $(\eta,w_1,...,w_n)$ of $\mathbb{R}^{n+1}$ such that $g(w_i,w_j)=\delta_{ij}$ and $g(\eta,w_i)=0$ for $i,j=1,..,n$
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