1 \documentclass[12pt]{article}

     2 \title{Matrices and Solution of Equations}

     3 \author{FOSSEE}

     4 \begin{document}

     5 \date{}

     6 \vspace{-1in}

     7 \begin{center}

     8 \LARGE{Matrices and Solution of Equations}\\

     9 \large{FOSSEE}

    10 \end{center}

    11 \section{Matrices}

    12 Inputting a Matrix

    13 \begin{verbatim}

    14 In [1]: A = matrix([[1, 2, 3],[4, 5, 6]])

    15 \end{verbatim}

    16 Matrix Operations

    17 \begin{verbatim}

    18 In [1]: A.T # Transpose

    19 In [2]: sum(A) # Sum of all elements

    20 In [3]: A+B # Addition

    21 In [1]: A*B # Product

    22 In [1]: inv(A) # Inverse

    23 In [1]: det(A) # Determinant

    24 \end{verbatim}

    25 

    26 Eigen Values and Eigen Vectors

    27 \begin{verbatim}

    28 In [1]: eig(A) #Eigen Values and Vectors

    29 In [2]: eigvals(A) #Eigen Values 

    30 \end{verbatim}

    31 Norm

    32 \begin{verbatim}

    33 In [1]: norm(A)

    34 \end{verbatim}

    35 Single Value Decomposition

    36 \begin{verbatim}

    37 In [1]: svd(A)

    38 \end{verbatim}

    39 Solving a set of equations

    40 \begin{verbatim}

    41 In [1]: A = matrix([...]) # Input Equation Coefficient Matrix   

    42 In [2]: b = matrix([...]) # Equation Target Values

    43 In [3]: x = solve(A, b)

    44 In [4]: Ax = A*x

    45 \end{verbatim}

    46 \end{document}

    47