Spacing between two math environments (gather and align)

Question

Currently, I am using gather and align environments when I want to write down several math equations in a single environment. When I have several of them, it works fine when there is a text between them, but the spacing is too much when there is no text between them:

\usepackage{mathtools}
\newcommand\algn[1]{\begin{align*}#1\end{align*}}
\newcommand\gthr[1]{\begin{gather*}#1\end{gather*}}
\newcommand{\ind}[1]{\mathbbold{#1}}
\DeclareMathOperator{\rank}{rank}
\newcommand{\trp}{\text{t}}
\DeclarePairedDelimiter\norm{\lVert}{\rVert}


\gthr{
    \sum_{n\in\ind{n}}m_n
    = \rank\langle \Lambda \rangle
    = \rank\langle T\Lambda T^{\trp} \rangle
    = \rank \langle \Delta^{1/2}A\Delta^{1/2} \rangle
    = \rank \langle A \rangle  
  }
  \algn{
    f^{\trp}Af
    & = f^{\trp}\Delta^{-1/2}(\Delta^{1/2}A\Delta^{1/2})\Delta^{-1/2}f\\
    &= (T^{\trp}\Delta^{-1/2}f)^{\trp}\Lambda (T^{\trp}\Delta^{-1/2}f)\\
    & = \sum_{r\in\ind{r}}\lambda_r (T_{,r}^{\trp}\Delta^{-1/2}f)^2\\
    & = \sum_{n\in\ind{n}}\lambda_n \norm{P_n^{\trp}\Delta^{-1/2}f}^2
  }

The top is the gather environment and the below is the align environment, and there is no text between them. I cannot incorporate the top equation in the align environment since I cannot center it properly. I want to reduce the spacing without using vspace every time. I have find a similar problem here Avoiding extra vertical space between groups of equation environments, but it did not work for me; when using align*, it ruined the horizontal positioning of the equations. Any help would be appreciated.

Answer 1

\documentclass{article}

\usepackage{amsmath}

\def\ind{?????}
\def\rank{???}
\def\trp{???}
\def\norm{???}
\begin{document}

aligned in gather
\begin{gather*}
    \sum_{n\in\ind{n}}m_n
    = \rank\langle \Lambda \rangle
    = \rank\langle T\Lambda T^{\trp} \rangle
    = \rank \langle \Delta^{1/2}A\Delta^{1/2} \rangle
    = \rank \langle A \rangle  
\\
\begin{aligned}
    f^{\trp}Af
    & = f^{\trp}\Delta^{-1/2}(\Delta^{1/2}A\Delta^{1/2})\Delta^{-1/2}f\\
    &= (T^{\trp}\Delta^{-1/2}f)^{\trp}\Lambda (T^{\trp}\Delta^{-1/2}f)\\
    & = \sum_{r\in\ind{r}}\lambda_r (T_{,r}^{\trp}\Delta^{-1/2}f)^2\\
    & = \sum_{n\in\ind{n}}\lambda_n \norm{P_n^{\trp}\Delta^{-1/2}f}^2
 \end{aligned}
\end{gather*}

\end{document}