let x=(x_{1},x_{2},...,x_{n})



Express the quadratic form S{_{x}}^{2} in the matrix notation x^{T}Ax, where A is symmetric.

How do i do this? its getting ugly if i only try to expand S{_{x}}^{2}
so i tried it for n=2 to get some hint of what the matrix A would be. Well i got the matrix for n=2 but i can't figure out how it would be for an arbitary n.

this is what i got for n=2 : A = \begin{bmatrix}\frac{1}{2}&-\frac{1}{2}\\-\frac{1}{2}&\frac{1}{2}\end{bmatrix}