Graphics and brackets not vertically aligned within align environment

Question

I'm trying to include small graphics within an equation setting (they're little diagrams of mathematical knots), using \includegraphics within the \begin{align} environment. The graphics themselves are contained within angular brackets (< and >), but they will make up part of a bigger equation that will include ( and [ brackets also. The graphics are about the size that \Bigg< would contain them nicely.

My problem is that, in the pdf output, the graphics are not aligned nicely with any of the brackets. Instead, the very bottom of the graphic is in line with the middle of the brackets, which doesn't look great! I've tried using both \left< to set the size automatically and \Bigg< to do it manually, but either way, its still all vertically unaligned.

I wasn't sure how to link in an image into to my worked example, but I've uploaded it as per the instructions here trefoil.png. I guess if its downloaded and saved as 'trefoil.png' it should still work. Apologies if there is an easier way of doing it, is my first post and wasn't sure!

\documentclass[a4paper,12pt, fleqn]{amsart}
%
\usepackage{fullpage}
\usepackage{graphicx}
\usepackage{hyperref}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{float}
\usepackage{amsmath}
\usepackage{toolbox}
%
\begin{document}
%
\begin{align*}
\left< \includegraphics[scale=0.02]{trefoil.png} \right> &=A\left<
\includegraphics[scale=0.02]{trefoil.png} \right> + A^{-1}\left<
\includegraphics[scale=0.02]{trefoil.png}\right>
\end{align*}
\end{document}

This is what the output ends up looking like

Thanks a lot in advance for any help!

Answer 1

I encapsulate the \includegraphics inside a \vcenter{\hbox{}}, since I am in math mode already and want the images to be centered about the math axis. I changed scale= to height/width specs, since in demo mode, the scale parameter does not really apply.

In the MWE below, I incorporate this process into a new macro \Includegraphics[]{} (with a capital I).

\documentclass[a4paper,12pt, fleqn]{amsart}
%
\usepackage{fullpage}
\usepackage[demo]{graphicx}
\usepackage{hyperref}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{float}
\usepackage{amsmath}
%\usepackage{toolbox}
%
\newcommand\Includegraphics[2][]{\vcenter{\hbox{\includegraphics[#1]{#2}}}}
\begin{document}
%
\begin{align*}
\left< \Includegraphics[width=1cm,height=1cm]{trefoil.png} \right> &=A\left<
\Includegraphics[width=1.5cm,height=1.5cm]{trefoil.png} \right> + A^{-1}\left<
\Includegraphics[width=.8cm,height=.8cm]{trefoil.png}\right>
\end{align*}
\end{document}

Answer 2

Just for completeness here is a solution based on adjustbox:

\documentclass[a4paper,12pt, fleqn]{amsart}
%
\usepackage{graphicx}
% overload \includegraphics with extra options
\usepackage[export]{adjustbox}
\usepackage{hyperref}
 %
\begin{document}
%
\begin{equation*}
 = A\left<
      \includegraphics[scale=0.1,valign=c]{example-image}
    \right> + 
    A^{-1}\left<\includegraphics[scale=0.1]{example-image}\right>
\end{equation*}
\end{document}

Answer 3

Try to shift image with raisebox:

\documentclass[a4paper,12pt, fleqn]{amsart}
%
\usepackage{graphicx}
\usepackage{hyperref}
%
\begin{document}
%
\begin{align*}
\left< \raisebox{-1em}{\includegraphics[scale=0.1]{example-image}} \right> 
    & = A\left<\includegraphics[scale=0.1]{example-image} \right> + 
        A^{-1}\left<\includegraphics[scale=0.1]{example-image}\right>
\end{align*}
\end{document}

Used only on left side of equations, it gives: