Bringing the (square) brackets to the same height

Question

Consider the .tex extract from below:

\begin{equation*}
A=U\Lambda U^T=\left[\begin{array}{ccc}
&   &  \\
u_1 & \cdots  & u_n \\
&  & 
\end{array}\right]\left[\begin{array}{ccc}
 \lambda_1 &  &  \\
 & \ddots  &  \\
&  & \lambda_n
\end{array}\right]\left[\begin{array}{ccc}
& u_1^T  &  \\
& \vdots  &  \\
& u_n^T & 
\end{array}\right],
\end{equation*}

As you may notice, the surrounding square brackets are not of the same height. How could one achieve the above expression with the same bracket height? (the expression within should be intact)

Answer 1

You can use some extra space by \\[3pt] for first and second lines.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
A=U\Lambda U^T=\left[\begin{array}{ccc}
&   &  \\[3pt]
u_1 & \cdots   & u_n \\[3pt]
&  &
\end{array}\right]\left[\begin{array}{ccc}
 \lambda_1 &  &  \\
 & \ddots  &  \\
&  & \lambda_n
\end{array}\right]\left[\begin{array}{ccc}

& u_1^T  &  \\
& \vdots  &  \\
& u_n^T &

\end{array}\right],
\end{equation*}
\end{document}