Aligning arrays within arrays within another array

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} 

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}[2][]{%
  #1\big[ & #2 & \big]
}
\newenvironment{rowarray}[2][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}