Equations including ``tikzpicture``

Question

With the following codes

\documentclass[12pt,a4paper]{report}
\usepackage{amsfonts,amsmath,amssymb,graphicx,amsthm,xcolor,tikz}
\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}

I get

Howerver I want to replace [] by || and chage the place of the minus -. Also I want to add them in equations as the picture shows

I tried with \begin{align*} .. & = \\ &= \end{align*} but it does not work.

Answer 1

The brackets are drawn manually, so you just need to modify (simplify) how they are drawn. E.g. \draw[thick] (mtrx-4-1.south west) -- (mtrx-2-1.north west); -- a single line from the bottom left corner of one cell, to the top left of another cell.

To move the minus signs, literally just move the minus signs in the code to a new row at the end of the matrix.

Note also the addition of the baseline key, as specified in use of tikzpicture matrix in align or gather environment, do get the proper vertical alignment.

Finally, the align* environment clashes with a TikZ matrix because for both, the & character has special meaning. To fix that, you can tell TikZ to use something else as the column separator with ampersand replacement. The common thing to use is \&, but you could use other macros as well. See that in the example below I added ampersand replacement=\& to the \matrix options, and I used \& inside the matrix, for example a_1 \& b_1 \& c_1 \& a_1 \& a_2 \\

\documentclass[12pt,a4paper]{report}
\usepackage{amsfonts,amsmath,amssymb,amsthm,tikz}
\usetikzlibrary{calc,matrix}
\begin{document}
\begin{align}
D &=
\begin{tikzpicture}[
baseline=-\the\dimexpr\fontdimen22\textfont2\relax,
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},
                 ampersand replacement=&amp;]
{
|[red]|+  &amp; |[red]|+  &amp; |[red]| +
 \[3.3mm,between origins]
a_1 &amp; b_1 &amp; c_1 &amp; a_1 &amp; a_2         \
a_2 &amp; b_2 &amp; c_2 &amp; a_2 &amp; b_2         \
a_3 &amp; b_3 &amp; c_3 &amp; a_3 &amp; b_3         \
|[blue]|- &amp; |[blue]|- &amp; |[blue]|- \
};
\draw[thick]  (mtrx-4-1.south west) -- (mtrx-2-1.north west);
\draw[thick] (mtrx-4-3.south east)  -- (mtrx-2-3.north east);
\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} \
 &= a+b+c\dots
\end{align}
\end{document}