quadratic function associated with a linear functionalQuadraticFunctionAssociatedWithALinearFunctional2003-10-15 01:06:072004-04-15 03:10:07Definition\usepackage{graphicx}
%\usepackage{xypic}
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\newcommand{\Z}{\mathbbmss{Z}}
\newcommand{\C}{\mathbbmss{C}}
\newcommand{\R}{\mathbbmss{R}}
\newcommand{\Q}{\mathbbmss{Q}}
\newcommand{\mathbb}[1]{\mathbbmss{#1}}
\newcommand{\figura}[1]{\begin{center}\includegraphics{#1}\end{center}}
\newcommand{\figuraex}[2]{\begin{center}\includegraphics[#2]{#1}\end{center}}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 $\varphi:V\to\R$
given by
\[\varphi(v)=\frac{1}{2}\|v\|^2-f(v)\]