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!
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1this is very opinion based question and actually is not related to (la) tex problems.– ZarkoDec 16, 2018 at 20:10
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1I 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 MarinhoDec 16, 2018 at 20:30
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than pleas show us what you try so far and provide at least a sketch what you like to obtain ...– ZarkoDec 16, 2018 at 21:19
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This doesn't exactly give you what you ask, but it may be a good starting point: tex.stackexchange.com/questions/168035/…– Steven B. SegletesDec 18, 2018 at 11:41
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That was good! It gave me some hints of how i'm going to proceed. I just needed this start, actually. Awesome!– Italo MarinhoDec 18, 2018 at 19:21
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1 Answer
This is an example using TikZ:
% 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
