# Mathematical symbol: An operator as a map from a vector space into itself

My professor had a nice notation that he used for operators on vector spaces that I thought was clear. It wasn't something like $L: \mathcal{V} \to \mathcal{V}$ but rather a hooked arrow that reinforced that concept that $L$ is a map from $\mathcal{V}$ into itself.

Here is an example of exactly what I am looking for:

• Welcome to TeX.SX! Are you meaning \hookrightarrow? – egreg Jan 29 '16 at 22:02
• Hi. No I am looking more for something along the lines of what is picture here: emojipedia-us.s3.amazonaws.com/cache/e2/dd/… but with the upper line being equal length to the lower line. – Johnver Jan 29 '16 at 23:11
• \hookleftarrow? – Sigur Jan 30 '16 at 0:03

Load \usepackage{mathabx} and then

$L: \mathcal{V} \righttoleftarrow$


For more symbols, check here.

• That is very nice. Thank you. Do you know if there is one with less curvature? – Johnver Jan 30 '16 at 0:16
• @Johnver, I don't think so. Please, check the link I posted above. – Sigur Jan 30 '16 at 0:18

Here is a possibility formed by superimposing a \supset symbol with a small arrowhead using \lefteqn. I used \blacktriangleleft scaled by 50% for the arrowhead.

Then I scaled the whole symbol to 85% (you could adjust this) and wrapped it in a \mathbin for spacing. Note also the use of \colon instead of : for proper spacing of functions.

\documentclass{article}

\usepackage{amssymb} % for \blacktriangleleft symbol
\usepackage{graphicx} % for \scalebox command

\newcommand{\toitself}{\mathbin{\scalebox{.85}{%
\lefteqn{\scalebox{.5}{$\blacktriangleleft$}}\raisebox{.34ex}{$\supset$}}}}

\begin{document}

$L\colon\mathcal{V}\toitself\mathcal{V}$

\end{document}