How to remove unnecessary space after flalign* environment

Question

I was wondering whether it would be possible to remove some unnecessary space after flalign* environment. I tried using \belowdisplayskip, but to no avail.

Below is the sample input.

{\setlength{\abovedisplayskip}{0pt}
\begin{flalign*}
x\mathbf{e}_1 + y\mathbf{e}_2 &= x\mathbf{f}_2 + y(-\mathbf{f}_1 - \mathbf{f}_2) &\\
  &= -y\mathbf{f}_1 + (x-y)\mathbf{f}_2 &\\
  &= w\mathbf{f}_1 + z\mathbf{f}_2  &
\end{flalign*}}
where $w = -y$ and $z = x - y$.

Here's the corresponding output:

Answer 1

You miss setting also \belowdisplayskip. However, as it's clear from the image, a spurious space will be inserted. You're better served with a new environment:

\documentclass{article}
\usepackage{amsmath}

\newenvironment{nospaceflalign*}
 {\setlength{\abovedisplayskip}{0pt}\setlength{\belowdisplayskip}{0pt}%
  \csname flalign*\endcsname}
 {\csname endflalign*\endcsname\ignorespacesafterend}

\begin{document}
Some irrelevant text above
\begin{nospaceflalign*}
x\mathbf{e}_1 + y\mathbf{e}_2 &= x\mathbf{f}_2 + y(-\mathbf{f}_1 - \mathbf{f}_2) &\\
  &= -y\mathbf{f}_1 + (x-y)\mathbf{f}_2 &\\
  &= w\mathbf{f}_1 + z\mathbf{f}_2  &
\end{nospaceflalign*}
where $w = -y$ and $z = x - y$.
\end{document}

Using \csname flalign*\endcsname in this case is necessary because the environment has a * in its name and the \begin{flalign*} form can't be used for technical reasons related to how amsmath processes alignment environments.

With \ignorespacesafterend we solve the spurious space issue. If later you want to modify the rendering, it will be easier to act on the definition, rather than on the document.