1

Here's a very general question: how would you guys write out a tutorial on matrix multiplication? Maybe with indicative arrows in order to show which line associates with its correspondent column, I really don't know how I would typeset these on LaTeX. Could you kindly give me some suggestions? Thanks in advance!

  • 1
    this is very opinion based question and actually is not related to (la) tex problems. – Zarko Dec 16 '18 at 20:10
  • 1
    I think it actually is, if you follow the way I've asked: how could I correlate two matrices with arrows, for example, in a way I could correlate the terms that'd be multiplied. I couldn't figure out myself how would I do such a thing. – Italo Marinho Dec 16 '18 at 20:30
  • than pleas show us what you try so far and provide at least a sketch what you like to obtain ... – Zarko Dec 16 '18 at 21:19
  • This doesn't exactly give you what you ask, but it may be a good starting point: tex.stackexchange.com/questions/168035/… – Steven B. Segletes Dec 18 '18 at 11:41
  • That was good! It gave me some hints of how i'm going to proceed. I just needed this start, actually. Awesome! – Italo Marinho Dec 18 '18 at 19:21
2

This is an example using TikZ:

enter image description here

% Author : Alain Matthes
% Source : http://altermundus.com/pages/examples.html
\documentclass[]{article}

\usepackage[utf8]{inputenc}
\usepackage[upright]{fourier}
\usepackage{tikz}
\usetikzlibrary{matrix,arrows,decorations.pathmorphing}
\begin{document}

% l' unite
\newcommand{\myunit}{1 cm}
\tikzset{
    node style sp/.style={draw,circle,minimum size=\myunit},
    node style ge/.style={circle,minimum size=\myunit},
    arrow style mul/.style={draw,sloped,midway,fill=white},
    arrow style plus/.style={midway,sloped,fill=white},
}

\begin{tikzpicture}[>=latex]
% les matrices
\matrix (A) [matrix of math nodes,%
             nodes = {node style ge},%
             left delimiter  = (,%
             right delimiter = )] at (0,0)
{%
  a_{11} & a_{12} & \ldots & a_{1p}  \\
  \node[node style sp] {a_{21}};%
         & \node[node style sp] {a_{22}};%
                  & \ldots%
                           & \node[node style sp] {a_{2p}}; \\
  \vdots & \vdots & \ddots & \vdots  \\
  a_{n1} & a_{n2} & \ldots & a_{np}  \\
};
\node [draw,below=10pt] at (A.south) 
    { $A$ : \textcolor{red}{$n$ rows} $p$ columns};

\matrix (B) [matrix of math nodes,%
             nodes = {node style ge},%
             left delimiter  = (,%
             right delimiter =)] at (6*\myunit,6*\myunit)
{%
  b_{11} & \node[node style sp] {b_{12}};%
                  & \ldots & b_{1q}  \\
  b_{21} & \node[node style sp] {b_{22}};%
                  & \ldots & b_{2q}  \\
  \vdots & \vdots & \ddots & \vdots  \\
  b_{p1} & \node[node style sp] {b_{p2}};%
                  & \ldots & b_{pq}  \\
};
\node [draw,above=10pt] at (B.north) 
    { $B$ : $p$ rows \textcolor{red}{$q$ columns}};
% matrice résultat
\matrix (C) [matrix of math nodes,%
             nodes = {node style ge},%
             left delimiter  = (,%
             right delimiter = )] at (6*\myunit,0)
{%
  c_{11} & c_{12} & \ldots & c_{1q} \\
  c_{21} & \node[node style sp,red] {c_{22}};%
                  & \ldots & c_{2q} \\
  \vdots & \vdots & \ddots & \vdots \\
  c_{n1} & c_{n2} & \ldots & c_{nq} \\
};
% les fleches
\draw[blue] (A-2-1.north) -- (C-2-2.north);
\draw[blue] (A-2-1.south) -- (C-2-2.south);
\draw[blue] (B-1-2.west)  -- (C-2-2.west);
\draw[blue] (B-1-2.east)  -- (C-2-2.east);
\draw[<->,red](A-2-1) to[in=180,out=90]
  node[arrow style mul] (x) {$a_{21}\times b_{12}$} (B-1-2);
\draw[<->,red](A-2-2) to[in=180,out=90]
  node[arrow style mul] (y) {$a_{22}\times b_{22}$} (B-2-2);
\draw[<->,red](A-2-4) to[in=180,out=90]
  node[arrow style mul] (z) {$a_{2p}\times b_{p2}$} (B-4-2);
\draw[red,->] (x) to node[arrow style plus] {$+$} (y)%
                  to node[arrow style plus] {$+\raisebox{.5ex}{\ldots}+$} (z)%
                  to (C-2-2.north west);


\node [draw,below=10pt] at (C.south) 
    {$ C=A\times B$ : \textcolor{red}{$n$ rows}  \textcolor{red}{$q$ columns}};

\end{tikzpicture}

\begin{tikzpicture}[>=latex]
% unit
% defintion of matrices
\matrix (A) [matrix of math nodes,%
             nodes = {node style ge},%
             left delimiter  = (,%
             right delimiter = )] at (0,0)
{%
  a_{11} &\ldots & a_{1k} & \ldots & a_{1p}  \\
    \vdots & \ddots & \vdots & \vdots & \vdots \\
  \node[node style sp] {a_{i1}};& \ldots%
         & \node[node style sp] {a_{ik}};%
                  & \ldots%
                           & \node[node style sp] {a_{ip}}; \\
  \vdots & \vdots& \vdots & \ddots & \vdots  \\
  a_{n1}& \ldots & a_{nk} & \ldots & a_{np}  \\
};
\node [draw,below] at (A.south) { $A$ : \textcolor{red}{$n$ rows} $p$ columns};
\matrix (B) [matrix of math nodes,%
             nodes = {node style ge},%
             left delimiter  = (,%
             right delimiter =)] at (7*\myunit,7*\myunit)
{%
  b_{11} &  \ldots& \node[node style sp] {b_{1j}};%
                  & \ldots & b_{1q}  \\
  \vdots& \ddots & \vdots & \vdots & \vdots \\
  b_{k1} &  \ldots& \node[node style sp] {b_{kj}};%
                  & \ldots & b_{kq}  \\
  \vdots& \vdots & \vdots & \ddots & \vdots \\
  b_{p1} &  \ldots& \node[node style sp] {b_{pj}};%
                  & \ldots & b_{pq}  \\
};
\node [draw,above] at (B.north) { $B$ : $p$ rows \textcolor{red}{$q$ columns}};
% matrice resultat
\matrix (C) [matrix of math nodes,%
             nodes = {node style ge},%
             left delimiter  = (,%
             right delimiter = )] at (7*\myunit,0)
{%
  c_{11} & \ldots& c_{1j} & \ldots & c_{1q} \\
  \vdots& \ddots & \vdots & \vdots & \vdots \\
    c_{i1}& \ldots & \node[node style sp,red] {c_{ij}};%
                  & \ldots & c_{iq} \\
  \vdots& \vdots & \vdots & \ddots & \vdots \\
  c_{n1}& \ldots & c_{nk} & \ldots & c_{nq} \\
};
\node [draw,below] at (C.south) 
    {$ C=A\times B$ : \textcolor{red}{$n$ rows}  \textcolor{red}{$q$ columns}};
% arrows
\draw[blue] (A-3-1.north) -- (C-3-3.north);
\draw[blue] (A-3-1.south) -- (C-3-3.south);
\draw[blue] (B-1-3.west)  -- (C-3-3.west);
\draw[blue] (B-1-3.east)  -- (C-3-3.east);
\draw[<->,red](A-3-1) to[in=180,out=90] 
    node[arrow style mul] (x) {$a_{i1}\times b_{1j}$} (B-1-3);
\draw[<->,red](A-3-3) to[in=180,out=90] 
    node[arrow style mul] (y) {$a_{ik}\times b_{kj}$}(B-3-3);
\draw[<->,red](A-3-5) to[in=180,out=90] 
    node[arrow style mul] (z) {$a_{ip}\times b_{pj}$}(B-5-3);
\draw[red,->] (x) to node[arrow style plus] {$+\raisebox{.5ex}{\ldots}+$} (y)%
                  to node[arrow style plus] {$+\raisebox{.5ex}{\ldots}+$} (z);
                  %
                  % to (C-3-3.north west);
\draw[->,red,decorate,decoration=zigzag] (z) -- (C-3-3.north west);
\end{tikzpicture}
\end{document}

% encoding : utf8
% format   : pdfLaTeX
% author   : Alain Matthes

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.