# Aligning arrays within arrays within another array

## Problem

The entry shows three matrices, one atop the other. Each matrix is made of three row vectors. Each row vector has three entries.

## Question

How to present the problem so that the three columns of entries are right aligned?

## Sample

The rightmost column is trivial. The center column is close. The first column is a disaster.

### Code

\documentclass[]{article}
\usepackage{amsmath}

\newcommand{\mat} {\left[\begin{array} {#1}#2 \end{array}\right]}
\newcommand{\ps}  {\phantom{-}}

\begin{document}
%
\begin{equation*}
\begin{array}{r}
%
\mat{r}{
\frac{1}{\sqrt{30}} \mat{rrr}{\ps1 & \ps\ps2 & \ps5} \\
\frac{1}{2\sqrt{6}} \mat{rrr}{\ps5 & \ps\ps0 & -1} \\
\frac{1}{\sqrt{195}}\mat{rrr}{-1 & \ps13 & -5} }  \\[35pt]
%
\mat{r}{
\frac{1}{\sqrt{30}} \mat{rrr}{-1 & \ps-2 & -5} \\
\frac{1}{2\sqrt{6}} \mat{rrr}{-5 & \ps\ps0 & \ps1} \\
\frac{1}{\sqrt{195}}\mat{rrr}{1 & -13 & \ps2} } \\[35pt]
%
\mat{r}{
\frac{1}{\sqrt{30}} \mat{rrr}{i & \ps2i & 5i} \\
\frac{1}{2\sqrt{6}} \mat{rrr}{5i & \ps0 & -i} \\
\frac{1}{\sqrt{195}}\mat{rrr}{1 & -13 & \ps5} }
%
\end{array}
%
\end{equation*}

\end{document}


### Output ## Efforts so far

Efforts have involved failed experiments with phantom characters. One such iteration is shown above.

## Related posts

Helpful, but could not glean solution.

Array within Align*

Alignment accross multiple arrays/vectors

Array alignment within align environment

Experiment with the various values: for the sake of the example, I set different ones for \extrarowheight in the three matrices.

\documentclass[]{article}
\usepackage{mathtools,array}

\newcommand{\rowvec}[]{%
#1\big[ & #2 & \big]
}
\newenvironment{rowarray}[0pt]
{%
\setlength{\extrarowheight}{#1}%
\array{@{} r @{} *{#2}{r} @{} l @{}}%
}
{\crcr\noalign{\kern\extrarowheight}\endarray}

\begin{document}

\begin{gather*}
\begin{bmatrix}
\begin{rowarray}[3pt]{3}
\rowvec[\frac{1}{\sqrt{30}}]{1 & 2 & 5} \\[\medskipamount]
\rowvec[\frac{1}{2\sqrt{6}}]{5 & 0 & -1} \\[\medskipamount]
\rowvec[\frac{1}{\sqrt{195}}]{-1 & 13 & -5}
\end{rowarray}
\end{bmatrix}
\\
\begin{bmatrix}
\begin{rowarray}[4pt]{3}
\rowvec[\frac{1}{\sqrt{30}}]{-1 & -2 & -5} \\[\medskipamount]
\rowvec[\frac{1}{2\sqrt{6}}]{-5 & 0 & 1} \\[\medskipamount]
\rowvec[\frac{1}{\sqrt{195}}]{1 & -13 & 2}
\end{rowarray}
\end{bmatrix}
\\
\begin{bmatrix}
\begin{rowarray}[5pt]{3}
\rowvec[\frac{1}{\sqrt{30}}]{i & 2i & 5i} \\[\medskipamount]
\rowvec[\frac{1}{2\sqrt{6}}]{5i & 0 & -i} \\[\medskipamount]
\rowvec[\frac{1}{\sqrt{195}}]{i & -13 & 5}
\end{rowarray}
\end{bmatrix}
\end{gather*}

\end{document} Maybe like this?

\documentclass[]{article}
\usepackage{mathtools}

\begin{document}
%
\begin{equation*}
\begin{array}{r}
%
\begin{bmatrix*}[r]
\frac{1}{\sqrt{30}} \bigl[\!\! & 1 & 2 & 5&\!\!\bigr] \\
\frac{1}{2\sqrt{6}} \bigl[\!\! &5 & 0 & -1&\!\!\bigr] \\
\frac{1}{\sqrt{195}}\bigl[\!\! &-1 & 13 & -5&\!\!\bigr]
\end{bmatrix*}  \\[35pt]
%
\begin{bmatrix*}[r]
\frac{1}{\sqrt{30}} \bigl[\!\! &-1 & -2 & -5&\!\!\bigr] \\
\frac{1}{2\sqrt{6}} \bigl[\!\! &-5 & 0 & 1&\!\!\bigr] \\
\frac{1}{\sqrt{195}}\bigl[\!\! &1 & -13 & 2&\!\!\bigr]
\end{bmatrix*}\\[35pt]
%
\begin{bmatrix*}[r]
\frac{1}{\sqrt{30}} \bigl[\!\! &\mathrm{i} & 2\mathrm{i} & 5\mathrm{i}&\!\!\bigr] \\
\frac{1}{2\sqrt{6}} \bigl[\!\! &5\mathrm{i} & 0 & -\mathrm{i}&\!\!\bigr] \\
\frac{1}{\sqrt{195}}\bigl[\!\! &\mathrm{i} & -13 & 5&\!\!\bigr]
\end{bmatrix*}
%
\end{array}
%
\end{equation*}

\end{document} A solution based on mathtools and bigdelim, which comes with multirow:

\documentclass[]{article}
\usepackage{mathtools}
\usepackage{array, bigdelim}

\begin{document}

\begin{gather*}
\begin{bmatrix*}[r]
\begin{array}{@{}r@{}rrr@{\,}r@{}}\\[-2ex]
\ldelim[{1}{*}[$\smash{\frac{1}{\sqrt{30}}}$] & 1 & 2 & 5 & \rdelim]{1}{*} \\[1.5ex]
%
\ldelim[{1}{*}[$\smash{\frac{1}{2\sqrt{6}}}$] & 5 & 0 & -1 & \rdelim]{1}{*}\\[1.5ex]
%
\ldelim[{1}{*}[$\smash{\frac{1}{195}}$] & -1 & 13 & -5 & \rdelim]{1}{*}\\
\end{array} \\[-2ex] \mbox{}
\end{bmatrix*}
\\[3ex]
\begin{bmatrix*}[r]
\begin{array}{@{}r@{}rrr@{\,}r@{}}\\[-2ex]
\ldelim[{1}{*}[$\smash{\frac{1}{\sqrt{30}}}$] & -1 & -2 & -5 & \rdelim]{1}{*} \\[1.5ex]
%
\ldelim[{1}{*}[$\smash{\frac{1}{2\sqrt{6}}}$] & -5 & 0 & 1 & \rdelim]{1}{*}\\[1.5ex]
%
\ldelim[{1}{*}[$\smash{\frac{1}{195}}$] & 1 & -13 & 5 & \rdelim]{1}{*}\\
\end{array} \\[-2ex] \mbox{}
\end{bmatrix*}
\\[3ex]
\begin{bmatrix*}[r]
\begin{array}{@{}r@{}rrr@{\,}r@{}}\\[-2ex]
\ldelim[{1}{*}[$\smash{\frac{1}{\sqrt{30}}}$] & i & 2i & 5i & \rdelim]{1}{*} \\[1.5ex]
%
\ldelim[{1}{*}[$\smash{\frac{1}{2\sqrt{6}}}$] & 5i & 0 & -i & \rdelim]{1}{*}\\[1.5ex]
%
\ldelim[{1}{*}[$\smash{\frac{1}{195}}$] & 1 & -13 & 5 & \rdelim]{1}{*}\\
\end{array} \\[-2ex] \mbox{}
\end{bmatrix*}
\end{gather*}

\end{document} 