Going through my lecture notes on geometry I find a definition of a Euclidean frame which doesn't seem to have been formed correctly (most likely written down wrong). So I've taken it upon myself to correct it and would like a check on it:
The ordered list $\{P_0, P_1, \ldots, P_{n+1}\} \subseteq \mathbb{E}^n$ is called a Euclidean frame if $\forall i, j, i \neq j: Q_i = P_i - P_0$ is such that $Q_i$ is orthogonal to $Q_j$ and $d(P_0, P_i) = 1$.
Is this okay? Or does it also require me to define what $Q_j$ is (perhaps as $Q_j = P_j - P_0$)?
Perhaps a way to rewrite this definition is as follows (I am not checking correctness, just changing the language).
The ordered list $\{P_0,P_1,\cdots,P_{n+1}\}\subseteq\mathbb{E}^n$ is called an Euclidean frame if the ordered list $\{Q_1,\cdots,Q_n\}$ where $Q_i=P_i-P_0$ has the property that for all $i\not=j$, $Q_i$ is orthogonal to $Q_j$ and $\|Q_i\|=1$.