# Wedge product symbol (exterior/alternating product)

This question has a similar title, but my question is different.

I would like to denote the kth exterior power similar to this:

\wedge is too small and \bigwedge is not only too big but also centered in a strange way:

Also, I don't like using \Lambda instead. I tried the relsize package, which provides the command \mathlarger{}. This is the result:

As you see, the wedge is still too small and there is too much space between the wedge and the letter k.

Do you know a good solution?

• dAdd a negative kerning to the exponent – something like \bigwedge^{\mkern-6mu k} (value to be adjusted to the real spacing). Mar 16, 2021 at 20:24
• BTW, if any of the answers helped you, it'd be nice if you could accept one of them by clicking on the checkmark symbol.
– chsk
May 3, 2021 at 9:58
• @chsk The problem is that I found several answers helpful. May 3, 2021 at 12:08
• @Filippo Ah, there's an easy solution to that. Just accept mine then. ;)
– chsk
May 3, 2021 at 12:16
• @chsk I know that was a joke, but I don't see the point in accepting one specific answer and therefore making it seem more helpful than the others. I think that all answers can be helpful to someone reading this question, especially because different methods have been used to solve the problem. May 3, 2021 at 15:49

You mention that a regular upper-case \Lambda won't cut it, but you could use a sans-serif one. I took the liberty of adapting @egreg's answer to this question:

\documentclass{article}
\usepackage[math-style=ISO]{unicode-math}
\defaultfontfeatures{Scale=MatchUppercase}
\setmathfontface\mathsans{TeX Gyre Heros}
\newcommand{\wedgeprod}{\mathsans{\mupLambda}}
\begin{document}
$$\wedgeprod^k V = {} \underbrace{ V \wedge V \dots \wedge V }_{\text{k times}}$$
\end{document}


This produces:

Definitely far from perfect, but better than nothing.

• There is a little v to the RHS :-) +1 Mar 16, 2021 at 21:47
• D'oh. Thanks for the pointer!
– chsk
Mar 16, 2021 at 21:48
• I vote your efforts and .....of the users :-) Mar 16, 2021 at 21:49
• Fixed & much appreciated!
– chsk
Mar 16, 2021 at 21:50

You can use a scaled down and raised up \bigwedge symbol.

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand{\exterior}[1]{\mathop{\mathpalette\exterior@{#1}}}
\newcommand{\exterior@}[2]{%
% raise to the baseline
\raisebox{\depth}{%
% select the script size relative to the current font
\fontsize{\sf@size}{0}%
% nullify the math surround
\m@th
% typeset \bigwedge, but using \textstyle in displays
$\ifx#1\displaystyle\textstyle\else#1\fi\bigwedge$}%
% the exponent, a bit nearer to the symbol
^{\mspace{-2mu}#2}%
% remove the \scriptspace
\kern-\scriptspace
}
\makeatother

\begin{document}

\begin{align}
\exterior{k}V &= {\underbrace{V\wedge V\wedge\dots\wedge V}_{\text{$k$ times}}}
\\
\exterior{k}(V) &= {\underbrace{V\wedge V\wedge\dots\wedge V}_{\text{$k$ times}}}
\\
a&=V_{\exterior{k}V}
\end{align}

\end{document}


Here I use a rotated text V to make the operator. Based on the OP's figures, I employed sffamily. Also, there appeared to be two sizes employed, so I mirrored that in \lamop and \lamopbold.

\documentclass{article}
\usepackage{amsmath,rotating}
\DeclareMathOperator\lamopbold{\rotatebox[origin=c]{180}{\textsf{V}}}
\DeclareMathOperator\lamop{\rotatebox[origin=c]{180}{\footnotesize\textsf{V}}}
\begin{document}
$\lamopbold^{\!k}(V) = \underbrace{V \lamop \dots \lamop V}_{\text{k times}}$
\end{document}


Here I add my proposal using a newcommand \bigw (of the standard symbol of Amsmath, \bigwedge) created with \scalebox contained in graphicx package. You can decrease the symbol \bigw changing the parameter of \scalebox{.95}[1].

\documentclass[12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{graphicx}

\newcommand\bigw{\scalebox{.95}[1]{$\bigwedge$}}
\begin{document}

$\bigw^{\!k}(V)=\underbrace{V \wedge V \dotsb \wedge V }_{k \text{ times}}$

\end{document}