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Is there a special term for an array consisting only of ones?

Sorry for the rather elementary question. I am getting into MapReduce programming and am trying to frame my code to be nice and neat.

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sum of the vectors of the canonical basis? –  user31280 May 24 '13 at 21:35
    
Not that I'm aware of. Why? –  Qiaochu Yuan May 24 '13 at 22:26
    
We call them «array of ones» :-) –  Mariano Suárez-Alvarez May 25 '13 at 0:05

2 Answers 2

up vote 2 down vote accepted

I have used, and seen used, the term "all-ones vector". It is typically notated however other vectors are being notated in your writing. For instance, if $\vec{x}$ is a vector, then the all-ones vector would be $\vec{1}$. Likewise, if $\mathbf{x}$ is a vector, then you'd write $\mathbf{1}$.

As an example, consider the average of a list of numbers. If the list is in vector $\mathbf{x}$, then the average can be written:

$\mathrm{average}(\mathbf{x}) = \dfrac{\mathbf{x}\cdot\mathbf{1}}{\mathbf{1}\cdot\mathbf{1}}$

where "$\cdot$" represents the standard dot product.

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Thank you! I am going to accept your answer on faith due to it being the top-ranked one ;) I do appreciate everyone's input though. –  verbsintransit May 28 '13 at 16:34
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I have also seen the use of the notation $\mathbf e$ to denote the (column) vector whose entries are all $1$, in analogy to the use of $\mathbf e_k$ to denote the $k$-th column of the identity matrix. –  J. M. May 29 '13 at 8:53

Not sure what you mean by "array". The $m\times n$ matrix whose entries are all ones could be denoted $1_{m\times n}$. Sometimes the $n\times n$ all-ones matrix is called $J_n$, or just $J$ if $n$ is understood from context.

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