# quadratic function associated with a linear functional

Let $V$ be a real hilbert space (and thus an inner product space), and let $f$ be a continuous linear functional on $V$. Then $f$ has an associated quadratic function $\varphi:V\to\mathbbmss{R}$ given by

 $\varphi(v)=\frac{1}{2}\|v\|^{2}-f(v)$
Title quadratic function associated with a linear functional QuadraticFunctionAssociatedWithALinearFunctional 2013-03-22 14:00:23 2013-03-22 14:00:23 drini (3) drini (3) 7 drini (3) Definition msc 11Exx msc 46Exx HilbertSpace InnerProductSpace