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Diffstat (limited to 'matrices/slides.tex')
| -rw-r--r-- | matrices/slides.tex | 66 |
1 files changed, 40 insertions, 26 deletions
diff --git a/matrices/slides.tex b/matrices/slides.tex index 8e58583..e0e8acd 100644 --- a/matrices/slides.tex +++ b/matrices/slides.tex @@ -1,4 +1,4 @@ -% Created 2010-10-12 Tue 14:28 +% Created 2010-11-07 Sun 16:18 \documentclass[presentation]{beamer} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} @@ -70,7 +70,7 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{itemize} \begin{verbatim} - In []: m1 = matrix([1, 2, 3, 4]) + In []: m1 = array([1, 2, 3, 4]) \end{verbatim} \begin{itemize} @@ -79,11 +79,25 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \begin{verbatim} In []: l1 = [[1,2,3,4],[5,6,7,8]] - In []: m2 = matrix(l1) + In []: m2 = array(l1) \end{verbatim} +\end{frame} +\begin{frame}[fragile] +\frametitle{Exercise 1} +\label{sec-3} + + Create a (2, 4) matrix \texttt{m3} +\begin{verbatim} + m3 = [[5, 6, 7, 8], + [9, 10, 11, 12]] +\end{verbatim} +\end{frame} +\begin{frame}[fragile] +\frametitle{Solution 1} +\label{sec-4} \begin{itemize} -\item A matrix is basically an array +\item m3 can be created as, \end{itemize} \begin{verbatim} @@ -92,7 +106,7 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{frame} \begin{frame}[fragile] \frametitle{Matrix operations} -\label{sec-3} +\label{sec-5} \begin{itemize} \item Element-wise addition (both matrix should be of order \texttt{mXn}) @@ -109,25 +123,25 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{frame} \begin{frame}[fragile] \frametitle{Matrix Multiplication} -\label{sec-4} +\label{sec-6} \begin{itemize} -\item Matrix Multiplication +\item Element-wise multiplication using \texttt{m3 * m2} \begin{verbatim} In []: m3 * m2 - Out []: ValueError: objects are not aligned \end{verbatim} -\item Element-wise multiplication using \texttt{multiply()} +\item Matrix Multiplication using \texttt{dot(m3, m2)} \begin{verbatim} - multiply(m3, m2) + In []: dot(m3, m2) + Out []: ValueError: objects are not aligned \end{verbatim} \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Matrix Multiplication (cont'd)} -\label{sec-5} +\label{sec-7} \begin{itemize} \item Create two compatible matrices of order \texttt{nXm} and \texttt{mXr} @@ -142,19 +156,19 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \item Creating another matrix of order \texttt{4 X 2} \begin{verbatim} - In []: m4 = matrix([[1,2],[3,4],[5,6],[7,8]]) + In []: m4 = array([[1,2],[3,4],[5,6],[7,8]]) \end{verbatim} \item Matrix multiplication \begin{verbatim} - In []: m1 * m4 + In []: dot(m1, m4) \end{verbatim} \end{itemize} \end{frame} \begin{frame} \frametitle{Recall from \texttt{array}} -\label{sec-6} +\label{sec-8} \begin{itemize} \item The functions @@ -178,7 +192,7 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{frame} \begin{frame}[fragile] \frametitle{More matrix operations} -\label{sec-7} +\label{sec-9} Transpose of a matrix \begin{verbatim} @@ -186,8 +200,8 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{verbatim} \end{frame} \begin{frame}[fragile] -\frametitle{Exercise 1 : Frobenius norm \& inverse} -\label{sec-8} +\frametitle{Exercise 2 : Frobenius norm \& inverse} +\label{sec-10} Find out the Frobenius norm of inverse of a \texttt{4 X 4} matrix. \begin{verbatim} @@ -196,7 +210,7 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} The matrix is \begin{verbatim} - m5 = matrix(arange(1,17).reshape(4,4)) + m5 = arange(1,17).reshape(4,4) \end{verbatim} \begin{itemize} @@ -215,8 +229,8 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{itemize} \end{frame} \begin{frame}[fragile] -\frametitle{Exercise 2: Infinity norm} -\label{sec-9} +\frametitle{Exercise 3 : Infinity norm} +\label{sec-11} Find the infinity norm of the matrix \texttt{im5} \begin{verbatim} @@ -230,7 +244,7 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{frame} \begin{frame}[fragile] \frametitle{\texttt{norm()} method} -\label{sec-10} +\label{sec-12} \begin{itemize} \item Frobenius norm @@ -247,7 +261,7 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{frame} \begin{frame}[fragile] \frametitle{Determinant} -\label{sec-11} +\label{sec-13} Find out the determinant of the matrix m5 \begin{verbatim} @@ -265,7 +279,7 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{frame} \begin{frame}[fragile] \frametitle{eigen values \& eigen vectors} -\label{sec-12} +\label{sec-14} Find out the eigen values and eigen vectors of the matrix \texttt{m5}. \begin{verbatim} @@ -300,7 +314,7 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{frame} \begin{frame}[fragile] \frametitle{Singular Value Decomposition (\texttt{svd})} -\label{sec-13} +\label{sec-15} $M = U \Sigma V^*$ \begin{itemize} @@ -318,7 +332,7 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{frame} \begin{frame} \frametitle{Summary} -\label{sec-14} +\label{sec-16} \begin{itemize} \item Matrices @@ -337,7 +351,7 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{frame} \begin{frame} \frametitle{Thank you!} -\label{sec-15} +\label{sec-17} \begin{block}{} \begin{center} |