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cardfrontfoot{Functional Analysis}

begin{flashcard}[Definition]{Lever celler}
  includegraphics[width=.8linewidth]{billeder/0604}
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begin{flashcard}[Definition]{Inner Product}

Let $X$ be a complex linear space. An emph{inner product} on $X$ is
a mapping that associates to each pair of vectors $x$, $y$ a scalar,
denoted $(x,y)$, that satisfies the following properties:

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begin{description}
item [Additivity] $(x+y,z) = (x,z) + (y,z)$,
item [Homogeneity] $(alpha : x, y) = alpha (x,y)$,
item [Symmetry] $(x,y) = overline{(y,x)}$,
item [Positive Definiteness] $(x,x) > 0$, when $xneq0$.
end{description}
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