Quadratic functional
= Quadratic functional
{title2=$I(v)=B(v,v)-2\ell(v)+c$}
A quadratic functional on a real vector space combines a <quadratic form> $B(v,v)$, a <linear functional> $\ell(v)$ and a constant. If $B$ is a symmetric <bounded bilinear form>, its <first variation> is $DI(v)[w]=2B(v,w)-2\ell(w)$. For a strictly positive $B$, an existing stationary point is the unique minimizer by the <quadratic variational principle for a symmetric positive operator>.