Why am I getting a vertical bar at the end of an equation?

Question

I am using Overleaf to write an equation. This is the latex:

\begin{equation*}
P_{0}\equiv \mathbf{E}\left[ \left( X_{0}-\hat{X}_{0}\right) \left( X_{0}-%
\hat{X}_{0}\right) ^{\intercal }\right] =\mathbf{E}\left[ \left( X_{0}-%
\mathbf{E}\left[ X_{0}\right] \right) \left( X_{0}-\mathbf{E}\left[ X_{0}%
\right] \right) ^{\intercal }\right] \equiv Cov\left( X_{0},X_{0}\right) .
\end{equation*}

Why am I getting a vertical bar at the end of the equation? (right after the final .)

I thought this may be since the equation is exactly as wide as the page.

I tried splitting the equation in two lines and the bar disappears. Is there a way to keep everything on one line removing the vertical line?

Here is some more information about the document I am writing:

\documentclass[%
    a4paper,
    corpo=12pt,
    oneside,
    stile=standard,
    tipotesi=magistrale,
    numerazioneromana, % roman numbering for appendixes and preambles, up to Table of Contents
    openright,
    cucitura=7mm,
]{toptesi}

\begin{document}
% ...
\end{document}

Packages I am using:

\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}

\usepackage{hyperref}

\usepackage[hyperref=true,backref=true,backend=biber,maxbibnames=9,maxcitenames=2,style=numeric,citestyle=numeric,sorting=none]{biblatex} 

\usepackage{adjustbox}
\usepackage{algorithm}
\usepackage{algpseudocode} 
\usepackage{amsfonts}          
\usepackage{amsmath}
\usepackage{amssymb}              
\usepackage{bm}                    
\usepackage{booktabs}            
\usepackage[labelfont=bf]{caption}
\usepackage{csquotes}
\usepackage{enumitem}
\usepackage{geometry}
\usepackage[
    toc,
    abbreviations,
    nonumberlist,
]{glossaries-extra}
\usepackage{graphicx}
\usepackage{listings}
\usepackage{lipsum}
\usepackage{makecell}
\usepackage{mathtools}
\usepackage{mfirstuc}
\usepackage[final]{microtype}
\usepackage{multirow}
\usepackage{nicefrac}
\usepackage{ragged2e}
\usepackage{siunitx}
\usepackage{subfig}
\usepackage{svg}
\usepackage{tabularx}
\usepackage{textcomp}
\usepackage{url}     
\usepackage{verbatim}
\usepackage{xcolor}

Answer 1

I get no “bar”. But I get an “Overfull \hbox” message.

You can avoid it by properly writing the expression with no \left and \right that create too big delimiters and excess space.

It's probably better to split the long equation in parts, doing a favor to your readers who will see more clearly the steps.

\documentclass[%
    a4paper,
    corpo=12pt,
    oneside,
    stile=standard,
    tipotesi=magistrale,
    numerazioneromana, % roman numbering for appendixes and preambles, up to Table of Contents
    openright,
    cucitura=7mm,
]{toptesi}

\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{adjustbox}
\usepackage{algorithm}
\usepackage{algpseudocode} 
\usepackage{amsfonts}          
\usepackage{amsmath}
\usepackage{amssymb}              
\usepackage{bm}                    
\usepackage{booktabs}            
\usepackage[labelfont=bf]{caption}
\usepackage{csquotes}
\usepackage{enumitem}
\usepackage{geometry}
\usepackage[
    toc,
    abbreviations,
    nonumberlist,
]{glossaries-extra}
\usepackage{graphicx}
\usepackage{listings}
\usepackage{lipsum}
\usepackage{makecell}
\usepackage{mathtools}
\usepackage{mfirstuc}
\usepackage[final]{microtype}
\usepackage{multirow}
\usepackage{nicefrac}
\usepackage{ragged2e}
\usepackage{siunitx}
\usepackage{subfig}
\usepackage{svg}
\usepackage{tabularx}
\usepackage{textcomp}
\usepackage{url}
\usepackage[
  hyperref=true,
  backref=true,
  backend=biber,
  maxbibnames=9,
  maxcitenames=2,
  style=numeric,
  citestyle=numeric,
  sorting=none,
]{biblatex} 

\usepackage{hyperref}


\begin{document}

\begin{equation*}
P_{0}
\equiv \mathbf{E}\bigl[(X_{0}-\hat{X}_{0}) (X_{0}-\hat{X}_{0})^{\intercal }\bigr]
=\mathbf{E}\bigl[(X_{0}-\mathbf{E}[X_{0}])(X_{0}-\mathbf{E}[X_{0}])^{\intercal}\bigr]
\equiv \operatorname{Cov}(X_{0},X_{0}) .
\end{equation*}

\begin{align*}
P_{0}
&\equiv \mathbf{E}\bigl[(X_{0}-\hat{X}_{0}) (X_{0}-\hat{X}_{0})^{\intercal }\bigr] \\
&=\mathbf{E}\bigl[(X_{0}-\mathbf{E}[X_{0}])(X_{0}-\mathbf{E}[X_{0}])^{\intercal}\bigr]\\
&\equiv \operatorname{Cov}(X_{0},X_{0}) .
\end{align*}

\end{document}

Do you really need all those packages? By the way, hyperref should go last. Particularly geometry sounds very strange with no option.

For the covariance operator, use \operatorname{Cov}; but if you use it several times, it's better to have

\DeclareMathOperator{\Cov}{Cov}

in the preamble and to use \Cov in the document.