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Consider a vector that is made up of N times the same element, stacked next to each other. I am having a hard time coming up with an elegant mathematical notation for indicating the repetitiveness of the elements, and the how often they repeat.

The best I could come up with is:

A vector with repeating elements

\documentclass{article}

\usepackage{mathtools}

\begin{document}
\[
    \underbrace{%
        \begin{pmatrix} 
            \Delta t \mathbf{a}_b &  \Delta t \mathbf{a}_b & \cdots & \Delta t
            \mathbf{a}_b 
        \end{pmatrix}%
     }_{N \times (\Delta t \mathbf{a}_b)} 
\]
\end{document}

Can you propose a way to make this clearer in LaTeX?

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2  
Since the element duplicate already suggest repetition, I would go for something like this. –  Werner Feb 6 at 20:09
1  
What does \mathbf{a}_b represent? –  egreg Feb 6 at 20:48
    
@egreg it's a row vector. –  Ingo Feb 7 at 8:30
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5 Answers

up vote 7 down vote accepted

This is very similar to another answer.

Since the duplication of elements already suggest repetition, I would merely highlight the number of elements/items in the vector:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}

\[
  \bigl( \underbrace{%
    \Delta t \mathbf{a}_b \quad \Delta t \mathbf{a}_b \quad \cdots \quad \Delta t \mathbf{a}_b
  }_{\text{$N$~elements}} \bigr)
\]

\end{document}
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I would simply write

enter image description here

\documentclass{article}

\usepackage{mathtools}

\begin{document}
\[
    \underbrace{%
        \begin{pmatrix}
            \Delta t \mathbf{a}_b &  \Delta t \mathbf{a}_b & \cdots & \Delta t
            \mathbf{a}_b
        \end{pmatrix}%
     }_{N \text{ times}}
\]
\end{document} 
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1  
IMO, the underbrace wrapping around the parentheses (rather than just their contents) can be confusing. At first glance, the reader might think that the whole vector, not the "building block", gets repeated N times (whatever that means). –  Jubobs Feb 6 at 20:27
1  
@Jubobs: Hence my suggested display... –  Werner Feb 6 at 20:30
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What you have might work, but here is an alternative (especially if you need it in \textstyle):

\documentclass{article}
\begin{document}
$[{(\Delta t\, \mathbf{a}_b)}_{\times N}] $
\end{document}

enter image description here

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Not necessarily implying that my proposition is superior, I think dot notation is old. You can also add a subscript to ones vector for size info or remove \cdot.

\documentclass{article}
\usepackage{mathtools,bbm}%Use your favorite font for bboard number
\begin{document}
\noindent
If someone defines $\mathbbm{1}$ as all-ones vector,
\[ \Delta t \cdot a_b \cdot \mathbbm{1}^T \]
\end{document}

enter image description here

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This would work if a_b was a scalar, but in my case it is a vector. Very interesting proposal, though. –  Ingo Feb 13 at 9:37
    
@Ingo It still works since it is a dyadic product. It's a vector times [1 1 ... 1] so still the repeated vectors as matrix columns. –  percusse Feb 13 at 9:56
    
Fair point! But I am not sure whether the simplicity of the notation is worth the risk of possible confusion among some readers. –  Ingo Feb 13 at 10:07
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I would like to propose yet another way:

\documentclass{article}

\usepackage{mathtools}

\begin{document}
% Row vector
\[
    \begin{pmatrix} 
        \Delta t \mathbf{a}_b  \stackrel{\times N}{\cdots\cdots}
    \end{pmatrix}
\]
% Column vector
\[
    \begin{pmatrix} 
        \Delta t \mathbf{a}_b^T\\
          \stackrel{\vdots}{\scriptstyle\times N}
    \end{pmatrix}
\]
\end{document}

Indicating repeating elements

There is an issue with the spacing for column vectors, though.

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