$q(x_1, x_2, x_3) = x_2x_3+{x_3}^2-{x_1}^2$ is a quadratic form on $\mathbb{R}^3$.
I need to find basis of $\mathbb{R}^3$ when $q$ is: $q = \delta_1{y_1}^2+\delta_2{y_2}^2 + \delta_3{y_3}^2$ when $|\delta_i| = 1$ for $i = 1, 2, 3$.
how I start to solve it?