# How to type tensor multiplication with vertical dots?

I want to type this equation in LaTeX. How do I type those vertical dots symbol?

• Use: $\vdots$. Nov 28 '13 at 8:23
• \vdots, also helpful: \rvdots Nov 28 '13 at 8:23
• \multido{\i=0+1}{3}{\psdot(0,\i)}? Nov 28 '13 at 8:26
• Nov 28 '13 at 10:07
• Use \mathbin{\vdots} to adjust the spacing around it. Nov 28 '13 at 11:07

These are obviously binary operators, so they should carry the same spacing. That is, use whatever works and then wrap it in \mathbin. While the original picture showed the bottom dots resting on the baseline, I think it would be more correct to center the symbols on the math axis (where the \cdot is placed). Here is a simple possibility, that does not allow for size changes in scripts, but does respect global size changes like \large.

\documentclass{article}

\def\onedot{$\mathsurround0pt\ldotp$}
\def\cddot{% two dots stacked vertically
\mathbin{\vcenter{\baselineskip.67ex
\hbox{\onedot}\hbox{\onedot}}%
}}%
\def\cdddot#1{% three dots
\mathbin{\vcenter{\baselineskip.67ex
\hbox{\onedot}\hbox{\onedot}\hbox{\onedot}%
}}%
}

\begin{document}
Test it:
$\mathbf{P} = \varepsilon_0 \left(\chi^{(1)} \cdot \mathbf{E} + \chi^{(2)} \cddot \mathbf{EE} + \chi^{(3)} \cdddot \mathbf{EEE} + \cdots \right)$
\end{document}


Allowing for changes in scripts is a good deal harder, but could be done with the aid of some of the internals of the mathdots package.

Here is my first try with the stackengine package:

\documentclass{article}
\usepackage{amsmath}
\usepackage{stackengine}
\newcommand{\tensorm}{%
% Uncomment below to adjust the gap between the dots
%\setstackgap{S}{0.6ex}%
\mathrel{\Shortstack{{.} {.} {.}}}}
\begin{document}
$\mathbf{P} = \epsilon_0 \left(\chi^{(1)} \cdot \mathbf{E}+\chi^{(2)} : \mathbf{EE}+\chi^{(3)}\tensorm \mathbf{EEE}+ \cdots \right)$
\end{document}


This should give you the result that you're looking for:

\mathbf{P} = \epsilon_0 \left(\chi^{(1)} \cdot \mathbf{E}+\chi^{(2)} : \mathbf{EE}+\chi^{(3)}\vdots \mathbf{EEE}+ \cdots \right)


Result:

• You'd better use \varepsilon and wrap the \vdots with some spacing, like \,. Nov 28 '13 at 10:21
• @m0nhawk not manual spacing, like \,, but one of the appropriates for math entities (\mathbin). Nov 29 '13 at 9:45