Proposition 4

*Let Q be a non-degenerate quadratic form on a finite-dimensional vector space E over A. Suppose that A is of characteristic $\neq 2$, and let $(x_1, \ldots, x_n)$ be an orthogonal basis of V. Let $T_1$ be the type of the quadratic form $Q_1$ defined on the vector space A and such that $Q_1(1) = 1$. The type of Q is then $\sum_{i=1}^n Q(x_i) \cdot T_1$.

Indeed the form Q is equivalent to