Let's consider an N dimensional vector where each coordinate takes the value 1. For example, for $N=5$ we have: $(1,1,1,1,1)$.
Does this type of vector have a name in the literature? Perhaps "unary?". Also, are there any conventions on how to refer to it in terms of notation? (e.g. $\mathbf{1}^T$?)
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$\begingroup$It's not quite common enough to have a standard notation, but a reasonably well-accepted notation would be something like $\mathbf{1}_n = (1, 1, \ldots, 1) \in \mathbb{R}^n$, and if you needed a column vector then you'd write $\mathbf{1}^\intercal_n$. It may sometimes be called the 1-vector of size $n$ or a size $n$ vector of 1s.
As such, it's the kind of thing that when you use it you would probably be best off defining it explicitly so that it's clear what you're doing with it.
$\endgroup$ $\begingroup$I'm not aware of any conventional terminology. However, vector of ones is pretty compact and seems to get the job done. Similarly, I'm not aware of any special notation. Were I using it, I'd just define some notation. For example, let $a \in \mathbb{R}^d$ denote the vector of ones (ie, $a = (1,\ldots, 1)$).
Of course, depending on the context, there could be special notation. That could represent the identity in something like the multiplicative group $\mathbb{Z}^× \times \mathbb{Z}^×$. Then the standard notation for an identity element would be used.
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