User:Comfr/sandbox/quad

For example, consider the ternary quadratic form:
 * $$\begin{align}

q(x,y,z) &= ax^2 + bxy + cy^2 + dyz + ez^2 + fxz \end{align}$$

where a, …, f are the coefficients.

The matrix determining this quadratic has one row and one column for each variable, and the matrix entries contain coefficients of those variables. In this case the variables are X, Y, Z.

The (x, x)-entry has a, the coefficient of $$x^2$$, and the remaining diagonal entries have the coefficients of the squares of the variables Y and Z. The (x, y)-entry and the (y, x)-entry both have b, the coefficient of xy. The remaining off-diagonal entries have similar symmetric entries, resulting in a symmetric matrix.