Vain question about cdot kerning

Question

I'm writing my first "real" paper in Latex, and one of my major pieces of notation involves item-wise multiplying the Nx1 vector \widehat{w} to the Nx1 vector \widehat{S}, and I've been using cdot to denote the non-matrix multiplication, so basically I am writing

(\widehat{w}\cdot\widehat{S})^{\intercal}\widetilde{H}(\widehat{w}\cdot\widehat{S})

a million times in my paper.

I am using cdot to avoid a lot of confusion that would result from just using \widehat{S}_w, or \widehat{w}\widehat{S} due to similar notation already in use in the paper. Basically I am complaining that the cdot adds a ton of space between the w and the S whereas really they are a single unit--a weighted S.

QUESTION: Is there any trick to shrink cdot or is there another bivariate function I could use to get the w and S to stick closer together? Can you help me make my paper prettier?

Thanks for any help.

Code:

\documentclass{article}
\usepackage{amssymb}
\begin{document}
\[(\widehat{w}\cdot\widehat{S})^{\intercal}\widetilde{H}(\widehat{w}\cdot\widehat{S})\]
\end{document}

Answer 1

Three suggestions:

1. See Why is \[ … \] preferable to $$?

2. Define a macro/command if you're using something multiple times. It promotes consistency and would make your life much easier if you decide to change things later on, even just a little bit. For example, \itemmul{<mat1>}{<mat2>}. As reference, see Consistent typography.

3. You can modify the spacing around a relation/operator to your liking by changing it into an ordinal symbol first, and then specifying the kerning using \mkern. Ordinals are obtained by wrapping the relation/operator in braces, like {\cdot} or using \mathord{\cdot}. Math kerning is specified in mus (or math units).

Using the above suggestions, here's a take on your spacing:

\documentclass{article}
\usepackage{amssymb}% http://ctan.org/pkg/amssymb
\newcommand{\itemmul}[2]{% \itemmul{<mat1>}{<mat2>}
  \widehat{#1}\mkern1mu{\cdot}\mkern1mu\widehat{#2}% itemwise-multiplication
}
\begin{document}
\[
  (\itemmul{w}{S})^{\intercal}\widetilde{H}(\itemmul{w}{S})
\]
\end{document}

Answer 2

You can reduce the space in between by using \kern-.2em.

\documentclass{article}
\usepackage{amssymb}
\begin{document}
\[(\widehat{w}\!\cdot\!\widehat{S})^{\intercal}\widetilde{H}(\widehat{w}\!\cdot\!\widehat{S})\]

\[(\widehat{w}\kern-.2em\cdot\kern-.2em\widehat{S})^{\intercal}\widetilde{H}(\widehat{w}\kern-.2em\cdot\kern-.2em\widehat{S})\]
\end{document}

You can define a macro to make things easier.

\newcommand*{\mycdot}{\kern-.2em\cdot\kern-.2em}

The mwe is

\documentclass{article}
\usepackage{amssymb}
\newcommand*{\mycdot}{\kern-.2em\cdot\kern-.2em}
\begin{document}
\[(\widehat{w}\!\cdot\!\widehat{S})^{\intercal}\widetilde{H}(\widehat{w}\!\cdot\!\widehat{S})\]

\[(\widehat{w}\kern-.2em\cdot\kern-.2em\widehat{S})^{\intercal}\widetilde{H}(\widehat{w}\kern-.2em\cdot\kern-.2em\widehat{S})\]

\[(\widehat{w}\mycdot\widehat{S})^{\intercal}\widetilde{H}(\widehat{w}\mycdot\widehat{S})\]

\end{document}