Wedge product symbol (exterior/alternating product)

Question

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?

Answer 1

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.

Answer 2

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}

Answer 3

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}

Answer 4

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}