Latex, how to align matrices

Question

I am working on an assignment. I have a matrix that I am trying to align, this is what it looks like.

I have two questions

1. How do I align these horizontally i.e how do I make columns 4,5 and 6 the same width as columns 1,2 and 3?
2. How to align these vertically i.e how do I make the lengths equal so that the top and bottom of all matrices align.

I am using the environment bsmallmatrix as I hope to apply this solution to a 24x24 matrix.

I have tried to use align* method described here and the arraystetch command described here, these did not get the desired results but it's possible I used them wrong.

Here is a sample of my Latex code.

\documentclass[a4 paper,11 pt]{article}
\usepackage{amsmath}
\usepackage{esvect}

\newenvironment{bsmallmatrix}
{\left[\begin{smallmatrix}}
    {\end{smallmatrix}\right]}

\begin{document}

\begin{equation}
    \frac{d^2}{dt^2} 
    \begin{bsmallmatrix}
        X_e \\
        Y_e \\
        Z_e \\
        X'_e \\
        Y'_e \\
        Z'_e
    \end{bsmallmatrix}
    =
    \begin{bsmallmatrix}
        0 & 0 & 0 & 1 & 0 & 0 \\
        0 & 0 & 0 & 0 & 1 & 0  \\
         0 & 0 & 0 & 0 & 0 & 1 \\
        \ddot{\vv{r}}_{e_{x}} & 0 & 0 & 0 & 0 & 0 \\
        0 & \ddot{\vv{r}}_{e_{y}} & 0 & 0 & 0 & 0 \\
        0 & 0 & \ddot{\vv{r}}_{e_{z}} & 0 & 0 & 0\\ 
    \end{bsmallmatrix}
    \begin{bsmallmatrix}
        X_e \\
        Y_e \\
        Z_e \\
        X'_e \\
        Y'_e \\
        Z'_e 
    \end{bsmallmatrix}
\end{equation}

\end{document}

Thanks in advance

Answer 1

I propose using \bracketMatrixstack from the tabstackengine package. The row baselineskip and column gap are settable, and one can also ask that all columns be the same width (based on widest column content). The cell style may also be specified, here to \scriptstyle.

\documentclass[a4 paper,11 pt]{article}
\usepackage{amsmath}
\usepackage{esvect}
\usepackage{tabstackengine}
\TABstackMath
\TABstackMathstyle{\scriptstyle}% CELL STYLE
\setstackgap{L}{9pt}% ROW BASELINESKIP
\setstacktabbedgap{1pt}% INTER-COLUMN GAP
\fixTABwidth{T}% MAKE ALL COLUMNS EQUAL WIDTH
\begin{document}
\begin{equation}
    \frac{d^2}{dt^2} 
    \bracketMatrixstack{
        X_e \\
        Y_e \\
        Z_e \\
        X'_e \\
        Y'_e \\
        Z'_e
    }
    =
    \bracketMatrixstack{
        0 & 0 & 0 & 1 & 0 & 0 \\
        0 & 0 & 0 & 0 & 1 & 0  \\
         0 & 0 & 0 & 0 & 0 & 1 \\
        \ddot{\vv{r}}_{e_{x}} & 0 & 0 & 0 & 0 & 0 \\
        0 & \ddot{\vv{r}}_{e_{y}} & 0 & 0 & 0 & 0 \\
        0 & 0 & \ddot{\vv{r}}_{e_{z}} & 0 & 0 & 0
    }
    \bracketMatrixstack{
        X_e \\
        Y_e \\
        Z_e \\
        X'_e \\
        Y'_e \\
        Z'_e 
    }
\end{equation}
\end{document}