Recompute the following Gram matrix for the weighted inner product $\langle x,y\rangle=x_1y_1+\frac{1}{2}x_2y_2+\frac{1}{3}x_3y_3+\frac{1}{4}x_4y_4$:
$$\left[\begin{array}{cc}2&-2&-1&0\\-2&5&2&2\\-1&2&2&3\\0&2&3&13\end{array}\right]$$
I have no problem finding Gram matrices, but how do I recompute this Gram matrix that I've found.
