How to prove $x^T\Sigma x$ is quadratic? where $\Sigma$ is covariant varible(symmetric matrix)
I did simple calculation with 3x2 matrix , 2x2 covariance, 2x3 matrix. the result is 3x3 matrix. But how to prove it's quadrtic?
$x^T\Sigma x = \Sigma x_i a_{ij} x_j$ so what?