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quadratic function associated with a linear functional (Definition)

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

\begin{displaymath}\varphi(v)=\frac{1}{2}\Vert v\Vert^2-f(v)\end{displaymath}



"quadratic function associated with a linear functional" is owned by drini. [ full author list (3) | owner history (3) ]
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See Also: Hilbert space, inner product space
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Cross-references: function, linear functional, continuous, inner product space, Hilbert space, real

This is version 4 of quadratic function associated with a linear functional, born on 2003-10-15, modified 2004-04-15.
Object id is 4853, canonical name is QuadraticFunctionAssociatedWithALinearFunctional.
Accessed 1741 times total.

Classification:
AMS MSC: 11Exx (Forms and linear algebraic groups)
 46Exx (Linear function spaces and their duals)
Pending Errata and Addenda
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