--- a/day1/session4.tex Tue Oct 27 23:31:14 2009 +0530
+++ b/day1/session4.tex Wed Oct 28 11:15:49 2009 +0530
@@ -136,30 +136,73 @@
\begin{frame}[fragile]
\frametitle{Matrices: Initializing}
\begin{lstlisting}
- In []: a = matrix([[1,2,3],
- [4,5,6],
- [7,8,9]])
+In []: A = ([[5, 2, 4],
+ [-3, 6, 2],
+ [3, -3, 1]])
- In []: a
- Out[]:
- matrix([[1, 2, 3],
- [4, 5, 6],
- [7, 8, 9]])
+In []: A
+Out[]: [[5, 2, 4],
+ [-3, 6, 2],
+ [3, -3, 1]]
\end{lstlisting}
\end{frame}
\subsection{Basic Operations}
+
+\begin{frame}[fragile]
+\frametitle{Transpose of a Matrix}
+\begin{lstlisting}
+In []: linalg.transpose(A)
+Out[]:
+matrix([[ 5, -3, 3],
+ [ 2, 6, -3],
+ [ 4, 2, 1]])
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Sum of all elements}
+ \begin{lstlisting}
+In []: linalg.sum(A)
+Out[]: 17
+ \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Matrix Addition}
+ \begin{lstlisting}
+In []: B = matrix([[3,2,-1],
+ [2,-2,4],
+ [-1, 0.5, -1]])
+
+In []: linalg.add(A, B)
+Out[]:
+matrix([[ 8. , 4. , 3. ],
+ [-1. , 4. , 6. ],
+ [ 2. , -2.5, 0. ]])
+ \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Matrix Multiplication}
+\begin{lstlisting}
+In []: linalg.multiply(A, B)
+Out[]:
+matrix([[ 15. , 4. , -4. ],
+ [ -6. , -12. , 8. ],
+ [ -3. , -1.5, -1. ]])
+\end{lstlisting}
+\end{frame}
+
\begin{frame}[fragile]
\frametitle{Inverse of a Matrix}
-
\begin{small}
\begin{lstlisting}
In []: linalg.inv(A)
Out[]:
-matrix([[ 0.07734807, 0.01657459, 0.32044199],
- [ 0.09944751, -0.12154696, -0.01657459],
- [-0.02762431, -0.07734807, 0.17127072]])
-
+array([[ 0.28571429, -0.33333333, -0.47619048],
+ [ 0.21428571, -0.16666667, -0.52380952],
+ [-0.21428571, 0.5 , 0.85714286]])
\end{lstlisting}
\end{small}
\end{frame}
@@ -167,16 +210,8 @@
\begin{frame}[fragile]
\frametitle{Determinant}
\begin{lstlisting}
- In []: linalg.det(a)
- Out[]: -9.5171266700777579e-16
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Computing Norms}
-\begin{lstlisting}
- In []: linalg.norm(a)
- Out[]: 16.881943016134134
+In []: det(A)
+Out[]: 42.0
\end{lstlisting}
\end{frame}
@@ -184,19 +219,41 @@
\frametitle{Eigen Values and Eigen Matrix}
\begin{small}
\begin{lstlisting}
- In []: linalg.eigvals(a)
- Out[]: array([1.61168440e+01, -1.11684397e+00, -1.22196337e-15])
-
- In []: linalg.eig(a)
- Out[]:
- (array([ 1.61168440e+01, -1.11684397e+00, -1.22196337e-15]),
- matrix([[-0.23197069, -0.78583024, 0.40824829],
- [-0.52532209, -0.08675134, -0.81649658],
- [-0.8186735 , 0.61232756, 0.40824829]]))
+In []: linalg.eig(A)
+Out[]:
+(array([ 7., 2., 3.]),
+ matrix([[-0.57735027, 0.42640143, 0.37139068],
+ [ 0.57735027, 0.63960215, 0.74278135],
+ [-0.57735027, -0.63960215, -0.55708601]]))
\end{lstlisting}
\end{small}
\end{frame}
+\begin{frame}[fragile]
+\frametitle{Computing Norms}
+\begin{lstlisting}
+ In []: linalg.norm(A)
+ Out[]: 10.63014581273465
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Single Value Decomposition}
+ \begin{small}
+ \begin{lstlisting}
+In []: linalg.svd(A)
+Out[]:
+(matrix([[-0.13391246, -0.94558684, -0.29653495],
+ [ 0.84641267, -0.26476432, 0.46204486],
+ [-0.51541542, -0.18911737, 0.83581192]]),
+ array([ 7.96445022, 7. , 0.75334767]),
+ matrix([[-0.59703387, 0.79815896, 0.08057807],
+ [-0.64299905, -0.41605821, -0.64299905],
+ [-0.47969029, -0.43570384, 0.7616163 ]]))
+ \end{lstlisting}
+ \end{small}
+\end{frame}
+
\section{Solving linear equations}
\begin{frame}[fragile]
@@ -219,7 +276,9 @@
\frametitle{Solving using Matrices}
Let us now look at how to solve this using \kwrd{matrices}
\begin{lstlisting}
- In []: A = matrix([[3,2,-1],[2,-2,4],[-1, 0.5, -1]])
+ In []: A = matrix([[3,2,-1],
+ [2,-2,4],
+ [-1, 0.5, -1]])
In []: b = matrix([[1], [-2], [0]])
In []: x = linalg.solve(A, b)
In []: Ax = dot(A, x)
@@ -251,9 +310,18 @@
So what did we learn??
\begin{itemize}
\item Matrices
+ \begin{itemize}
+ \item Transpose
+ \item Addition
+ \item Multiplication
+ \item Inverse of a matrix
+ \item Determinant
+ \item Eigen values and Eigen matrix
+ \item Norms
+ \item Single Value Decomposition
+ \end{itemize}
\item Solving linear equations
\end{itemize}
\end{frame}
\end{document}
-