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I'm about to use this diagram to make computing 3x3 determinants clear and easy for my students. I tried to add this picture to my lecture but it's blurred due to the bad quality of the picture. So i want to create exactly the same figure using latex. I've searched and read a few topics about highlighting elements and diagonals in matrix but it does not work in this case. I want to add plus signs and minus signs as in the picture, and highlight elements in the matrice with elements outside the matrice. I appreciate all your help and your advice. Thank you in advance ! enter image description here

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4 Answers 4

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An alternative "pure" TikZ solution:

\documentclass[border=1mm,tikz]{standalone}
\usetikzlibrary{calc,matrix}

    \begin{document}
\begin{tikzpicture}[
strip/.style args = {#1/#2}{
    draw=#1, very thin, fill=#1, opacity=0.2,
    text width=#2,% will be calculated in path
    rounded corners,% only if you like them ...
    minimum height=1em,% adjust to desired height,
    inner xsep=-1mm,% adjust to desired length of strip
    inner ysep=2mm,
    yshift=-0.6ex,
    sloped},
                    ]
\matrix (mtrx)  [matrix of math nodes,
                 column sep=1em,   
                 nodes={text height=2ex,text width=2ex}]
{
|[red]|+
    & |[red]|+
          & \color{red}+\color{blue}- 
                & |[blue]|- 
                      & |[blue]|-   \\
a_1 & b_1 & c_1 & a_1 & a_2   \\
a_2 & b_2 & c_2 & a_2 & b_2   \\
a_3 & b_3 & c_3 & a_3 & b_3   \\
};
\draw[thick] (mtrx-2-1.north) -| (mtrx-4-1.south -- (mtrx-4-1.south);
\draw[thick] (mtrx-2-3.north) -| (mtrx-4-3.south -- (mtrx-4-3.south);
\path let   \p1 = (mtrx-4-1.center),
            \p2 = (mtrx-2-4.center),
            \n1 = {veclen(\y2-\y1,\x2-\x1)} in
      (mtrx-4-1.center) -- node[strip=blue/\n1] {} (mtrx-2-3.center)
      (mtrx-4-2.center) -- node[strip=blue/\n1] {} (mtrx-2-4.center)
      (mtrx-4-3.center) -- node[strip=blue/\n1] {} (mtrx-2-5.center)
%
      (mtrx-2-1.center) -- node[strip=red/\n1] {} (mtrx-4-3.center)
      (mtrx-2-2.center) -- node[strip=red/\n1] {} (mtrx-4-4.center)
      (mtrx-2-3.center) -- node[strip=red/\n1] {} (mtrx-4-5.center);
\end{tikzpicture}
    \end{document}

enter image description here

If you like to have different colors, you can defined similarly as this do @MyUserlsThis in his/her answer.

Edit: I wasn't aware for this answer, @egreg thank you for point it. Considered it, the solutions is more simple (and beautiful): 

\documentclass[border=1mm,tikz]{standalone}
\usetikzlibrary{calc,matrix}

        \begin{document}
\begin{tikzpicture}[
strip/.style = {
    draw=#1,%color
    line width=1em, opacity=0.2,
    line cap=round ,% only if you like them ...
                            },
                    ]
\matrix (mtrx)  [matrix of math nodes,
                 column sep=1em,   
                 nodes={text height=2ex,text width=2ex}]
{
|[red]|+
    & |[red]|+
          & \color{red}+\color{blue}- 
                & |[blue]|- 
                      & |[blue]|-   \\
a_1 & b_1 & c_1 & a_1 & a_2   \\
a_2 & b_2 & c_2 & a_2 & b_2   \\
a_3 & b_3 & c_3 & a_3 & b_3   \\
};
\draw[thick] (mtrx-2-1.north) -| (mtrx-4-1.south west) 
                              -- (mtrx-4-1.south);
\draw[thick] (mtrx-2-3.north) -| (mtrx-4-3.south east)
                              -- (mtrx-4-3.south);
\path[draw,strip=red,shorten <=-1mm]
    (mtrx-4-1.center) edge (mtrx-2-3.center)
    (mtrx-4-2.center) edge (mtrx-2-4.center)
    (mtrx-4-3.center)  --  (mtrx-2-5.center);
\path[draw,strip=blue,shorten >=-1mm]
    (mtrx-2-1.center) edge (mtrx-4-3.center)
    (mtrx-2-2.center) edge (mtrx-4-4.center)
    (mtrx-2-3.center)  --  (mtrx-4-5.center);

\end{tikzpicture}
    \end{document}

which gives:

enter image description here

Edit (2): Regarding to comment of @BarbaraBenton: signs + and - can be moved nearly line width reducing distance between the first and second row. This and also lookout, when strips is rectangular one can obtain with next MWE (where also colors are interchanged):

\documentclass[border=1mm,tikz]{standalone}
\usetikzlibrary{calc,matrix}

        \begin{document}
\begin{tikzpicture}[
strip/.style = {
    draw=#1,%color
    line width=1em, opacity=0.2,
    shorten <=-2mm,shorten >=-2mm,
                            },
                    ]
\matrix (mtrx)  [matrix of math nodes,
                 column sep=1em,
                 nodes={text height=1ex,text width=2ex}]
{
|[red]|+
    & |[red]|+
          & \color{red}+\color{blue}-
                & |[blue]|-
                      & |[blue]|-   \\[3.3mm,between origins]
a_1 & b_1 & c_1 & a_1 & a_2         \\
a_2 & b_2 & c_2 & a_2 & b_2         \\
a_3 & b_3 & c_3 & a_3 & b_3         \\
};
\draw[thick] (mtrx-2-1.north) -| (mtrx-4-1.south west)
                              -- (mtrx-4-1.south);
\draw[thick] (mtrx-2-3.north) -| (mtrx-4-3.south east)
                              -- (mtrx-4-3.south);
\path[draw,strip=blue]
    (mtrx-4-1.center) edge (mtrx-2-3.center)
    (mtrx-4-2.center) edge (mtrx-2-4.center)
    (mtrx-4-3.center)  --  (mtrx-2-5.center);
\path[draw,strip=red]
    (mtrx-2-1.center) edge (mtrx-4-3.center)
    (mtrx-2-2.center) edge (mtrx-4-4.center)
    (mtrx-2-3.center)  --  (mtrx-4-5.center);
\end{tikzpicture}
    \end{document}

enter image description here

Of course, there is still place to make fine adjustment. For example smaller signs + and -, or different positioning, or etc, but something should be left to OP (if he will accept the answer).

Edit (3): For use with document class beamer, here is complete and many time tested MWE (with recent Beamer: version 3.36):

    \documentclass{beamer} 
\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{calc,matrix}

        \begin{document}
\begin{frame}[fragile]
\begin{tikzpicture}[
strip/.style = {
    draw=#1,%color
    line width=1em, opacity=0.2,
    shorten <=-2mm,shorten >=-2mm,
                            },
                    ]
\matrix (mtrx)  [matrix of math nodes,
                 column sep=1em,
                 nodes={text height=1ex,text width=2ex}]
{
|[red]|+
    & |[red]|+
          & \color{red}+\color{blue}-
                & |[blue]|-
                      & |[blue]|-   \\[3.3mm,between origins]
a_1 & b_1 & c_1 & a_1 & a_2         \\
a_2 & b_2 & c_2 & a_2 & b_2         \\
a_3 & b_3 & c_3 & a_3 & b_3         \\
};
\draw[thick] (mtrx-2-1.north) -| (mtrx-4-1.south west)
                              -- (mtrx-4-1.south);
\draw[thick] (mtrx-2-3.north) -| (mtrx-4-3.south east)
                              -- (mtrx-4-3.south);
\path[draw,strip=blue]
    (mtrx-4-1.center) edge (mtrx-2-3.center)
    (mtrx-4-2.center) edge (mtrx-2-4.center)
    (mtrx-4-3.center)  --  (mtrx-2-5.center);
\path[draw,strip=red]
    (mtrx-2-1.center) edge (mtrx-4-3.center)
    (mtrx-2-2.center) edge (mtrx-4-4.center)
    (mtrx-2-3.center)  --  (mtrx-4-5.center);
\end{tikzpicture}
\end{frame}
    \end{document}
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15
  • Thanks for the answer, I didn't know the \matrix tikz command.
    – MyUserIsThis
    Jul 26, 2015 at 10:08
  • the pluses and minuses are not placed in proper relation to the bars they should be associated with, and in the second example, the colors are reversed.
    – barbara beeton
    Jul 26, 2015 at 12:06
  • @barbarabeeton, regarding colors: rush is newer good ... fortunate<y, this is easy to correct (and use colors on own taste), But the signs + and -: to put them closer to lines is require some effort. I will try do this.
    – Zarko
    Jul 26, 2015 at 12:32
  • I use beamer class and i put the code in a frame but i did not work. It seems to me that Tikz does not work in beamer. Any suggestion ?
    – Bungbu
    Jul 27, 2015 at 15:58
  • @Bungbu, it works. Tested. Instead of first two lines in MWE use: \documentclass{beamer} \usepackage{tikz} ....
    – Zarko
    Jul 27, 2015 at 18:17
9

After playing around with tikz, I could get it, I believe, decently. I'm just a tikz beginner, so I am 100% sure this can be done better, without needing so much fine-tuning of positions. You can adjust all positions and colors though:

\documentclass{article}

\usepackage{tikz}
\usepackage{amsmath}
\usepackage{xcolor}
\definecolor{myblue}{rgb}{0,0,0.8}
\definecolor{myred}{rgb}{0.8,0,0}


\begin{document}
\begin{tikzpicture}
\node[fill=none,draw=none] (matrix)
{
\begin{minipage}{\textwidth}
\[ \begin{bmatrix} 
a_1 & b_1 & c_1 \\
a_2 & b_2 & c_2 \\
a_3 & b_3 & c_3
\end{bmatrix}
\begin{matrix}
a_1 & b_1 \\
a_2 & b_2 \\
a_3 & b_3
\end{matrix} \]
\end{minipage}
};
\draw[myblue,fill=myblue,opacity=0.2] (-1.4,-0.4)--(0.25,0.6)--(0.4,0.4)--(-1.25,-0.6);
\draw[myblue,fill=myblue,opacity=0.2] (-0.7,-0.4)--(0.9,0.6)--(1.05,0.4)--(-0.55,-0.6);
\draw[myblue,fill=myblue,opacity=0.2] (0,-0.4)--(1.55,0.6)--(1.7,0.4)--(0.15,-0.6);
\draw[myred,fill=myred,opacity=0.2] (-1.4,0.4)--(0.25,-0.6)--(0.4,-0.4)--(-1.25,0.6);
\draw[myred,fill=myred,opacity=0.2] (-0.7,0.4)--(0.85,-0.6)--(1.0,-0.4)--(-0.55,0.6);
\draw[myred,fill=myred,opacity=0.2] (0,0.4)--(1.55,-0.6)--(1.7,-0.4)--(0.15,0.6);
\node[above of=matrix,xshift=-1.3cm,yshift=-0.2cm] {\textcolor{myred}{$+$}};
\node[above of=matrix,xshift=-0.6cm,yshift=-0.2cm] {\textcolor{myred}{$+$}};
\node[above of=matrix,xshift=-0cm,yshift=-0.2cm] {\textcolor{myred}{$+$}};
\node[above of=matrix,xshift=0.4cm,yshift=-0.2cm] {\textcolor{myblue}{$-$}};
\node[above of=matrix,xshift=1cm,yshift=-0.2cm] {\textcolor{myblue}{$-$}};
\node[above of=matrix,xshift=1.6cm,yshift=-0.2cm] {\textcolor{myblue}{$-$}};
\end{tikzpicture}
\end{document}

enter image description here

EDIT: In view of the comment by barbara, I've tried to enlarge the space between rows, to make it a little easier to see. I've done it following exactly this: incrementing matrix space. The only problem is that the matrix's bracket is too tall (it ends up being above the plus and - signs), and I don't know how to fix it. I leave the code and result, and if anyone knows how to do so, I'll happily edit this. Or you can just increase the yshift value of the plus and minus signs to put them above the matrix.

\documentclass{article}

\usepackage{tikz}
\usepackage{amsmath}
\usepackage{xcolor}
\definecolor{myblue}{rgb}{0,0,0.8}
\definecolor{myred}{rgb}{0.8,0,0}

\begingroup
\renewcommand*{\arraystretch}{1.5}
% your pmatrix expression
\endgroup

\makeatletter
\renewcommand*\env@matrix[1][\arraystretch]{%
  \edef\arraystretch{#1}%
  \hskip -\arraycolsep
  \let\@ifnextchar\new@ifnextchar
  \array{*\c@MaxMatrixCols c}}
\makeatother

\begin{document}
\begin{tikzpicture}
\node[fill=none,draw=none] (matrix)
{
\begin{minipage}{\textwidth}
\[ \begin{bmatrix}[1.5] 
a_1 & b_1 & c_1 \\
a_2 & b_2 & c_2 \\
a_3 & b_3 & c_3
\end{bmatrix}
\begin{matrix}[1.5]
a_1 & b_1 \\
a_2 & b_2 \\
a_3 & b_3
\end{matrix} \]
\end{minipage}
};
\draw[myblue,fill=myblue,opacity=0.2] (-1.4,-0.7)--(0.2,0.75)--(0.35,0.55)--(-1.25,-0.9);
\draw[myblue,fill=myblue,opacity=0.2] (-0.7,-0.7)--(0.8,0.75)--(0.95,0.55)--(-0.55,-0.9);
\draw[myblue,fill=myblue,opacity=0.2] (0,-0.7)--(1.45,0.75)--(1.6,0.55)--(0.15,-0.9);
\draw[myred,fill=myred,opacity=0.2] (-1.4,0.55)--(0.25,-0.9)--(0.4,-0.7)--(-1.25,0.75);
\draw[myred,fill=myred,opacity=0.2] (-0.7,0.55)--(0.85,-0.9)--(1.0,-0.7)--(-0.55,0.75);
\draw[myred,fill=myred,opacity=0.2] (0,0.55)--(1.55,-0.9)--(1.7,-0.7)--(0.15,0.75);
\node[above of=matrix,xshift=-1.3cm,yshift=-0.1cm] {\textcolor{myred}{$+$}};
\node[above of=matrix,xshift=-0.6cm,yshift=-0.1cm] {\textcolor{myred}{$+$}};
\node[above of=matrix,xshift=-0cm,yshift=-0.1cm] {\textcolor{myred}{$+$}};
\node[above of=matrix,xshift=0.4cm,yshift=-0.1cm] {\textcolor{myblue}{$-$}};
\node[above of=matrix,xshift=1cm,yshift=-0.1cm] {\textcolor{myblue}{$-$}};
\node[above of=matrix,xshift=1.6cm,yshift=-0.1cm] {\textcolor{myblue}{$-$}};
\end{tikzpicture}
\end{document}

enter image description here

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  • Thank you. How can i lengthen or shorten the diagonal highlights ?
    – Bungbu
    Jul 26, 2015 at 8:16
  • @Bungbu The \draw lines are the ones drawing the rectangles, and the four pairs of numbers are the coordinates of the corners of each rectangle. If you want to change the sizes, you will have to change those coordinates and do some fine-tuning until you get the desired results.
    – MyUserIsThis
    Jul 26, 2015 at 10:05
  • very nice. i think a little more vertical space between the rows would improve the appearance, also, i interpret the plus signs as being applicable to the pink bars, so they might be placed a bit more to the left, along the axes of those bars; similarly for the minus signs and the blue bars, shifted a bit to the right. (shifting pluses and minuses may not be necessary if the bars are more upright as a result of additional vertical space.)
    – barbara beeton
    Jul 26, 2015 at 12:04
3

With {NiceMatrix} of nicematrix (≥ 5.16 2021-06-20) and Tikz to draw the rules.

\documentclass{article}
\usepackage{nicematrix}
\usepackage{tikz}

\begin{document}

$\begin{NiceMatrix}[columns-width=7mm]
\CodeBefore [create-cell-nodes]
    \begin{tikzpicture} 
      [line width=3.5mm, opacity=0.2, shorten < = -3mm, shorten > = -3mm]
      \draw [blue] (4-1.center) -- (2-3.center) ;
      \draw [blue] (4-2.center) -- (2-4.center) ;
      \draw [blue] (4-3.center) -- (2-5.center) ;
      \draw [red] (2-1.center) -- (4-3.center) ;
      \draw [red] (2-2.center) -- (4-4.center) ;
      \draw [red] (2-3.center) -- (4-5.center) ;
    \end{tikzpicture}
\Body
    \color{red} +   & \color{red} +   & \color{red}+\color{blue}-  & \color{blue}-   & \color{blue}- \\
    a_1 & b_1 & c_1 & a_1 & a_2   \\[2mm]
    a_2 & b_2 & c_2 & a_2 & b_2   \\[2mm]
    a_3 & b_3 & c_3 & a_3 & b_3   \\
\CodeAfter
    \SubMatrix[{2-1}{4-3}]
\end{NiceMatrix}$

\end{document}

You need several compilations (because of the PGF/Tikz nodes).

Output of the above code

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Combining

we can achieve this with TikZ-CD without having to draw over nodes.

Code

\documentclass{article}
\usepackage{tikz-cd,amsmath}
\usetikzlibrary{backgrounds,calc}
\tikzcdset{
  math matrix/.style={
    column sep=1.5*\the\arraycolsep, row sep=.3*\the\baselineskip,
    cells={nodes={font=\mathstrut, inner sep=+0pt, outer sep=+0pt}}},
  lr delim/.style={/tikz/every matrix/.append style={lr delim={#1}}}}
\tikzset{% https://tex.stackexchange.com/a/660470/16595
  lr delim/.style args={#1#2 and #3#4 around #5 to #6}{append after command={
    {{[local bounding box=@] (\tikzlastnode-#5.north west)
     (\tikzlastnode-#6.south east)}(@)[every left delimiter/.append style={#2},
                                      every right delimiter/.append style={#4},
                 late options={left delimiter={#1},right delimiter={#3}}]}[]}}}
\makeatletter
\let\tikzcd@ar@new@orig\tikzcd@ar@new
\def\tikzcd@ar@new@bg[#1]{% https://tex.stackexchange.com/a/664328/16595
  \pgfutil@g@addto@macro\tikzcd@savedpaths{%
    \pgfonlayer{background}\path[/tikz/commutative diagrams/.cd,every arrow,#1]%
    (\tikzcd@ar@start\tikzcd@startanchor)to(\tikzcd@ar@target\tikzcd@endanchor);
    \endpgfonlayer}\let\tikzcd@ar@new\tikzcd@ar@new@orig}
\tikzcdset{every diagram/.append code=%
  \def\bgar{\let\tikzcd@ar@new\tikzcd@ar@new@bg\tikzcd@arrow}}
\makeatother
\tikzcdset{
  highlight/.style 2 args={
    /tikz/arrows=-, draw opacity=.5, draw=#1!50, text=#1, line width=.95em,
    line cap=round, to path={let\p0=($(\tikztostart)-(\tikztotarget)$),
      \n0={atan2(\y0,\x0)} in (\tikztostart.\n0)--(\tikztotarget.\n0-180)
        node[pos=1.2]{$#2$}\tikztonodes}}}
\begin{document}
\[\begin{tikzcd}[math matrix, lr delim={[ and ] around 1-1 to 3-3},
  cells={nodes={align=center,text width=width("$a_0$")}},
  minus/.style={highlight={blue}{-}}, plus/.style={highlight={red}{+}}]
  a_1 & b_1 & c_1 & a_1 & b_1 \\
  a_2 & b_2 & c_2 & a_2 & b_2 \\
  a_3 \bgar[rruu, minus]
& b_3 \bgar[rruu, minus]
& c_3 \bgar[rruu, minus] \bgar[lluu, plus]
& a_3                    \bgar[lluu, plus]
& b_3                    \bgar[lluu, plus]
\end{tikzcd}\]

\newcommand*\mPlus[1] {\mathcolor{red} {#1}}
\newcommand*\mMinus[1]{\mathcolor{blue}{#1}}
\[ \det A = (\mPlus {a_1b_2c_3} + \mPlus {b_1c_2a_3} + \mPlus {c_1a_2b_3})
           -(\mMinus{a_3b_2c_1} + \mMinus{b_3c_2a_1} + \mMinus{c_3a_2b_1}) \]
\end{document}

Output

enter image description here

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