font size needs to be reduced

Question

How can I adjust the size of subscripts showing dimension of these matrices in following code.

Is there anything other than \tiny{.} that can be used for this purpose?

\documentclass{beamer}
\usepackage{amsmath}
\newcommand*{\vertbar}{\rule[1ex]{0.5pt}{2.5ex}}
\newcommand*{\horzbar}{\rule[.5ex]{2.5ex}{0.5pt}}

\begin{document}

\begin{frame}
\begin{align*}
\boldsymbol{A} =
\left[
  \begin{array}{ccc}
    \horzbar & \boldsymbol{a}_{1}^{\tiny{T}} & \horzbar\\
    \horzbar & \boldsymbol{a}_{2}^{\tiny{T}} & \horzbar\\
    & \vdots & \\
    \horzbar & \boldsymbol{a}_{k_1}^{\tiny{T}} & \horzbar
  \end{array}
\right]_{\tiny{ k_1 \times k_2}}\implies
vec (\boldsymbol{A}) = 
  \left[
  \begin{matrix}
   \boldsymbol{a}_{1}^{\tiny{T}}   & \boldsymbol{a}_{2}^{\tiny{T}}       & \cdots   & \boldsymbol{a}_{k_1}^{\tiny{T}}     
\end{matrix}
\right]_{\tiny{k_1 k_2 \times 1}}^T
\end{align*}
\end{frame}
\end{document}