I have read in various papers that we can write a Quadratic equation with symmetric matrix as a linear programming problem. For example
$$f(x)= x^T*Q*x + c$$
where Q=[2 0;0 3]; Now we can write $$Q=H^TH$$
So we can write
$$A=[I\quad Hx; x^TH^T \quad-c];$$ $$A= [1\quad 0\quad 1.4142x1; 0\quad 1\quad 1.7321x2; 1.4142x1\quad 1.7321x2\quad 1];$$
where I is identity matrix and the matrix A is linear in variables of vector x, rather than quadratic. Now determinant of A is exactly equal to the quadratic equation f(x).
But I have some problem in understanding the matrix A.
1) It has three equation. If I want to solve it for x1 and x2, the three equations doesn't hold.
2) How can I calculate the basis for the matrix A in x1 and x2?