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+%%
+%% This is file `samplecards.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% flashcards.dtx (with options: `sample')
+%%
+%% FlashCards LaTeX2e Class for Typesetting Double Sided Cards
+%% Copyright (C) 2000 Alexander M. Budge <ambudge@mit.edu>
+%%
+%% This program is free software; you can redistribute it and/or modify
+%% it under the terms of the GNU General Public License as published by
+%% the Free Software Foundation; either version 2 of the License, or
+%% (at your option) any later version.
+%%
+%% This program is distributed in the hope that it will be useful,
+%% but WITHOUT ANY WARRANTY; without even the implied warranty of
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+%% GNU General Public License for more details.
+%%
+%% You should have received a copy of the GNU General Public License
+%% along with this program (the file COPYING); if not, write to the
+%% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+%%
+%% \CharacterTable
+%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%% Digits \0\1\2\3\4\5\6\7\8\9
+%% Exclamation \! Double quote \" Hash (number) \#
+%% Dollar \$ Percent \% Ampersand \&
+%% Acute accent \' Left paren \( Right paren \)
+%% Asterisk \* Plus \+ Comma \,
+%% Minus \- Point \. Solidus \/
+%% Colon \: Semicolon \; Less than \<
+%% Equals \= Greater than \> Question mark \?
+%% Commercial at \@ Left bracket \[ Backslash \\
+%% Right bracket \] Circumflex \^ Underscore \_
+%% Grave accent \` Left brace \{ Vertical bar \|
+%% Right brace \} Tilde \~}
+%%
+\NeedsTeXFormat{LaTeX2e}[1996/12/01]
+\ProvidesFile{samplecards.tex}
+\documentclass[avery5388,grid,frame]{flashcards}
+
+\cardfrontstyle[\large\slshape]{headings}
+\cardbackstyle{empty}
+
+\begin{document}
+
+\cardfrontfoot{Functional Analysis}
+
+\begin{flashcard}[Definition]{Norm on a Linear Space \\ Normed Space}
+
+ A real-valued function $||x||$ defined on a linear space $X$, where
+ $x \in X$, is said to be a \emph{norm on} $X$ if
+
+ \smallskip
+
+ \begin{description}
+ \item [Positivity] $||x|| \geq 0$,
+ \item [Triangle Inequality] $||x+y|| \leq ||x|| + ||y||$,
+ \item [Homogeneity] $||\alpha x|| = |\alpha| \: ||x||$,
+ $\alpha$ an arbitrary scalar,
+ \item [Positive Definiteness] $||x|| = 0$ if and only if $x=0$,
+ \end{description}
+
+ \smallskip
+
+ where $x$ and $y$ are arbitrary points in $X$.
+
+ \medskip
+
+ A linear/vector space with a norm is called a \emph{normed space}.
+\end{flashcard}
+
+\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:
+
+ \medskip
+
+ \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 $x\neq0$.
+ \end{description}
+\end{flashcard}
+
+\begin{flashcard}[Definition]{Linear Transformation/Operator}
+
+ A transformation $L$ of (operator on) a linear space $X$ into a linear
+ space $Y$, where $X$ and $Y$ have the same scalar field, is said to be
+ a \emph{linear transformation (operator)} if
+
+ \medskip
+
+ \begin{enumerate}
+ \item $L(\alpha x) = \alpha L(x), \forall x\in X$ and $\forall$
+ scalars $\alpha$, and
+ \item $L(x_1 + x_2) = L(x_1) + L(x_2)$ for all $x_1,x_2 \in X$.
+ \end{enumerate}
+
+\end{flashcard}
+
+\end{document}
+
+\endinput
+%%
+%% End of file `samplecards.tex'.