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 $\phi :V\to ℝ$ given by

$$\phi (v)=\frac{1}{2}{\parallel v\parallel }^2-f(v)$$

Title	quadratic function associated with a linear functional
Canonical name	QuadraticFunctionAssociatedWithALinearFunctional
Date of creation	2013-03-22 14:00:23
Last modified on	2013-03-22 14:00:23
Owner	drini (3)
Last modified by	drini (3)
Numerical id	7
Author	drini (3)
Entry type	Definition
Classification	msc 11Exx
Classification	msc 46Exx
Related topic	HilbertSpace
Related topic	InnerProductSpace