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+#+LaTeX_CLASS: beamer
+#+LaTeX_CLASS_OPTIONS: [presentation]
+#+BEAMER_FRAME_LEVEL: 1
+
+#+BEAMER_HEADER_EXTRA: \usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent}
+#+COLUMNS: %45ITEM %10BEAMER_env(Env) %10BEAMER_envargs(Env Args) %4BEAMER_col(Col) %8BEAMER_extra(Extra)
+#+PROPERTY: BEAMER_col_ALL 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 :ETC
+
+#+LaTeX_CLASS: beamer
+#+LaTeX_CLASS_OPTIONS: [presentation]
+
+#+LaTeX_HEADER: \usepackage[english]{babel} \usepackage{ae,aecompl}
+#+LaTeX_HEADER: \usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet}
+
+#+LaTeX_HEADER: \usepackage{listings}
+
+#+LaTeX_HEADER:\lstset{language=Python, basicstyle=\ttfamily\bfseries,
+#+LaTeX_HEADER:  commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen},
+#+LaTeX_HEADER:  showstringspaces=false, keywordstyle=\color{blue}\bfseries}
+
+#+TITLE: Matrices
+#+AUTHOR: FOSSEE
+#+EMAIL:     
+#+DATE:    
+
+#+DESCRIPTION: 
+#+KEYWORDS: 
+#+LANGUAGE:  en
+#+OPTIONS:   H:3 num:nil toc:nil \n:nil @:t ::t |:t ^:t -:t f:t *:t <:t
+#+OPTIONS:   TeX:t LaTeX:nil skip:nil d:nil todo:nil pri:nil tags:not-in-toc
+
+* Outline
+  - Creating Matrices
+    - using direct data
+    - converting a list
+  - Matrix operations
+  - Inverse of matrix
+  - Determinant of matrix
+  - Eigen values and Eigen vectors of matrices
+  - Norm of matrix
+  - Singular Value Decomposition of matrices
+
+* Creating a matrix
+  - Creating a matrix using direct data
+  : In []: m1 = matrix([1, 2, 3, 4])
+  - Creating a matrix using lists
+  : In []: l1 = [[1,2,3,4],[5,6,7,8]]
+  : In []: m2 = matrix(l1)
+  - A matrix is basically an array
+  : In []: m3 = array([[5,6,7,8],[9,10,11,12]])
+
+* Matrix operations
+  - Element-wise addition (both matrix should be of order ~mXn~)
+    : In []: m3 + m2
+  - Element-wise subtraction (both matrix should be of order ~mXn~)
+    : In []: m3 - m2
+* Matrix Multiplication
+  - Matrix Multiplication
+    : In []: m3 * m2
+    : Out []: ValueError: objects are not aligned
+  - Element-wise multiplication using ~multiply()~
+    : multiply(m3, m2)
+
+* Matrix Multiplication (cont'd)
+  - Create two compatible matrices of order ~nXm~ and ~mXr~
+    : In []: m1.shape
+    - matrix m1 is of order ~1 X 4~
+  - Creating another matrix of order ~4 X 2~
+    : In []: m4 = matrix([[1,2],[3,4],[5,6],[7,8]])
+  - Matrix multiplication
+    : In []: m1 * m4
+* Recall from ~array~
+  - The functions 
+    - ~identity(n)~ - 
+      creates an identity matrix of order ~nXn~
+    - ~zeros((m,n))~ - 
+      creates a matrix of order ~mXn~ with 0's
+    - ~zeros_like(A)~ - 
+      creates a matrix with 0's similar to the shape of matrix ~A~
+    - ~ones((m,n))~
+      creates a matrix of order ~mXn~ with 1's
+    - ~ones_like(A)~
+      creates a matrix with 1's similar to the shape of matrix ~A~
+  Can also be used with matrices
+
+* More matrix operations
+  Transpose of a matrix
+  : In []: m4.T
+* Exercise 1 : Frobenius norm \& inverse
+  Find out the Frobenius norm of inverse of a ~4 X 4~ matrix.
+  : 
+  The matrix is
+  : m5 = matrix(arange(1,17).reshape(4,4))
+  - Inverse of A, 
+    - 
+     #+begin_latex
+       $A^{-1} = inv(A)$
+     #+end_latex
+  - Frobenius norm is defined as,
+    - 
+      #+begin_latex
+        $||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2}$
+      #+end_latex
+
+* Exercise 2: Infinity norm
+  Find the infinity norm of the matrix ~im5~
+  : 
+  - Infinity norm is defined as,
+    #+begin_latex
+       $max([\sum_{i} abs(a_{i})^2])$
+    #+end_latex
+* ~norm()~ method
+  - Frobenius norm
+    : In []: norm(im5)
+  - Infinity norm
+    : In []: norm(im5, ord=inf)
+* Determinant
+  Find out the determinant of the matrix m5
+  : 
+  - determinant can be found out using
+    - ~det(A)~ - returns the determinant of matrix ~A~
+* eigen values \& eigen vectors
+  Find out the eigen values and eigen vectors of the matrix ~m5~.
+  : 
+  - eigen values and vectors can be found out using
+    : In []: eig(m5)
+    returns a tuple of /eigen values/ and /eigen vectors/
+  - /eigen values/ in tuple
+    - ~In []: eig(m5)[0]~
+  - /eigen vectors/ in tuple
+    - ~In []: eig(m5)[1]~
+  - Computing /eigen values/ using ~eigvals()~
+    : In []: eigvals(m5)
+* Singular Value Decomposition (~svd~)
+  #+begin_latex
+    $M = U \Sigma V^*$
+  #+end_latex
+    - U, an ~mXm~ unitary matrix over K.
+    - 
+      #+begin_latex
+        $\Sigma$
+      #+end_latex
+	, an ~mXn~ diagonal matrix with non-negative real numbers on diagonal.
+    - 
+      #+begin_latex
+        $V^*$
+      #+end_latex
+	, an ~nXn~ unitary matrix over K, denotes the conjugate transpose of V.
+  - SVD of matrix ~m5~ can be found out as,
+    : In []: svd(m5)
+* Summary
+  - Matrices
+    - creating matrices
+  - Matrix operations
+  - Inverse (~inv()~)
+  - Determinant (~det()~)
+  - Norm (~norm()~)
+  - Eigen values \& vectors (~eig(), eigvals()~)
+  - Singular Value Decomposition (~svd()~)
+
+* Thank you!
+#+begin_latex
+  \begin{block}{}
+  \begin{center}
+  This spoken tutorial has been produced by the
+  \textcolor{blue}{FOSSEE} team, which is funded by the 
+  \end{center}
+  \begin{center}
+    \textcolor{blue}{National Mission on Education through \\
+      Information \& Communication Technology \\ 
+      MHRD, Govt. of India}.
+  \end{center}  
+  \end{block}
+#+end_latex
+
+