= Matrix representation of the symmetric bilinear form
{synonym}

Like the <matrix representation of a bilinear form>, it is a <matrix>, but now the matrix has to be a <symmetric matrix>.

We can then immediately see that the matrix is symmetric, then so is the form. We have:
$$
B(x,y) = x^T M y
$$
But because $B(x,y)$ is a <scalar>, we have:
$$
B(x,y) = B(x,y)^T
$$
and:
$$
B(x,y) = B(x,y)^T = (x^T M y)^T = y^T M^T x = y^T M^T x = y^T M x = B(y,x)
$$


Matrix representation of a symmetric bilinear form