Hyperref adds vertical space to equation environment

Question

When the length of the text prior to an equation environment approaches \textwidth, hyperref adds an extra vertical space, as illustrated by the following snapshot:

The corresponding code is

\documentclass[12pt,fleqn]{article}
\usepackage{a4}
\usepackage{amsmath}
\usepackage{hyperref}

\textwidth = 16cm
\setlength{\parskip}{1.5ex plus0.5ex minus0.5ex}
\setlength{\parindent}{0em}

\begin{document}
Suppose $\vec{T}$ is a lower triangular matrix. Then $\vec{T}^{T}$ is upper triangular. By Lemma 2.23921,
\begin{equation}
    \det(\vec{T}) = \det(\vec{T}^{T}) = [\vec{T}]_{11}[\vec{T}]_{22}\dotsb[\vec{T}]_{nn},
\end{equation}
as required.
\end{document}

Note that it seems to affect the equation environment only.

Since there is no apparent way to predetermine the occurrence the problem in the source code, I will have to manually scan the output text for the affected parts and replace equation with other math environments, such as gather, to circumvent the problem; clearly, this approach is suboptimal.

So, the question is, why does it only affect the equation environment but not other math environments? Is there a way fix this?

Answer 1

You're being unlucky, but also hyperref should do better.

\documentclass[12pt,a4paper,fleqn]{article}
\usepackage{amsmath}
\usepackage{etoolbox}
\usepackage{hyperref}

\BeforeBeginEnvironment{equation}{%
  \ifhmode\unskip\fi
}

\textwidth = 16cm
\setlength{\parskip}{1.5ex plus0.5ex minus0.5ex}
\setlength{\parindent}{0em}

\begin{document}

Suppose $\vec{T}$ is a lower triangular matrix. Then $\vec{T}^{T}$ is upper
triangular. By Lemma 2.23921,
\begin{equation}
    \det(\vec{T}) = \det(\vec{T}^{T}) = [\vec{T}]_{11}[\vec{T}]_{22}\dotsb[\vec{T}]_{nn},
\end{equation}
as required.

\end{document}

_{Note. I left your setting of \parindent and \parskip, but this doesn't mean I endorse them. To the contrary, I advice you not to use those settings.}

Answer 2

It seems that this is a bug in the hyperref package. When hyperref isn't loaded then the paragraph-part before display is ended by a space (after the comma at the end of the line in your excellent example) and then the \begin{equation} does \refstepcounter {equation} and then it expands to $$ which starts the display mode. The start of display mode executes TeX internal algorithm: it finalizes the current horizontal mode by \unskip (i.e. the mentioned space is removed) and does something similar like \par (i.e. the horizontal list is broken to the lines, horizontal mode is interrupted and the lines are contributed to the vertical list). Then the display math is typeset. Note, that this case (without the ending space in the horizontal mode, because it is removed) fits the paragraph-part exactly to one line.

When hyperref is loaded, it re-defines the \refstepcounter macro. Now, this macro advances the counter by one plus puts the hyperlink destination to the current mode. This current mode is horizontal mode and the destination is put after the mentioned space. This destination is realized by \penalty10000\hbox{...\pdfdest{...}} but this isn't important. The main result is that the internal \unskip action processed when display math is started cannot remove the mentioned space because there is a barrier in the form of hyperlink destination. And the horizontal mode is longer by the mentioned space in this case. Now, this horizontal list is broken to the two lines (the second line is empty) and after that, the display math is typeset.