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%Tutorial slides on Python.

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% Author: FOSSEE 

% Copyright (c) 2009, FOSSEE, IIT Bombay

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% Title page

\title[Basic Python]{Matrices, Solution of equations}

\author[FOSSEE] {FOSSEE}

\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}

\date[] {31, October 2009\\Day 1, Session 4}

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\begin{frame}

  \titlepage

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\begin{frame}

  \frametitle{Outline}

  \tableofcontents

%  \pausesections

\end{frame}

\section{Matrices}

\begin{frame}

\frametitle{Matrices: Introduction}

We looked at the Van der Monde matrix in the previous session,\\ 

let us now look at matrices in a little more detail.

\end{frame}

\subsection{Initializing}

\begin{frame}[fragile]

\frametitle{Matrices: Initializing}

\begin{lstlisting}

\end{lstlisting}

\end{frame}

\subsection{Basic Operations}

\begin{frame}[fragile]

\frametitle{Inverse of a Matrix}

\begin{small}

\begin{lstlisting}

In []: linalg.inv(A)

Out[]: 

\end{lstlisting}

\end{small}

\end{frame}

\begin{frame}[fragile]

\frametitle{Determinant}

\begin{lstlisting}

\end{lstlisting}

\end{frame}

\begin{frame}[fragile]

\frametitle{Eigen Values and Eigen Matrix}

\begin{small}

\begin{lstlisting}

\end{lstlisting}

\end{small}

\end{frame}

\section{Solving linear equations}

\begin{frame}[fragile]

\frametitle{Solution of equations}

Consider,

  \begin{align*}

    3x + 2y - z  & = 1 \\

    2x - 2y + 4z  & = -2 \\

    -x + \frac{1}{2}y -z & = 0

  \end{align*}

Solution:

  \begin{align*}

    x & = 1 \\

    y & = -2 \\

    z & = -2

  \end{align*}

\end{frame}

\begin{frame}[fragile]

\frametitle{Solving using Matrices}

Let us now look at how to solve this using \kwrd{matrices}

  \begin{lstlisting}

    In []: b = matrix([[1], [-2], [0]])

    In []: x = linalg.solve(A, b)

    In []: Ax = dot(A, x)

    In []: allclose(Ax, b)

    Out[]: True

  \end{lstlisting}

\end{frame}

\begin{frame}[fragile]

\frametitle{Solution:}

\begin{lstlisting}

In []: x

Out[]: 

array([[ 1.],

       [-2.],

       [-2.]])

In []: Ax

Out[]: 

matrix([[  1.00000000e+00],

        [ -2.00000000e+00],

        [  2.22044605e-16]])

\end{lstlisting}

\end{frame}

\section{Summary}

\begin{frame}

  \frametitle{Summary}

So what did we learn??

  \begin{itemize}

  \item Matrices

  \item Solving linear equations

  \end{itemize}

\end{frame}

\end{document}