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Is there a name generally accepted for vectors of the form $(0,\dots,0,1,0,\dots,0)\in \Bbb R^n$?

I understand this is one of the members of the orthonormal base of $\Bbb R^n$, but I believe that in the context I'm using. it this characterisation would be somewhat pedantic.

Also, is there a standard symbol to denote it? I was thinking of using $\mathbf{1}_{i^{*}}$, where $i^{*}$ stands for the position of the $1$.

amWhy
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Patricio
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    $e_k$ is a popular designation for the $k$-th of these "basis vectors". – Angina Seng Sep 09 '20 at 14:09
  • @AnginaSeng: I would make that an answer. In fact, I was just about to write it. – Ross Millikan Sep 09 '20 at 14:13
  • This is a vector of the canonical basis $C={e_1,e_2, \dots ,e_n} \subseteq \mathbb{K^n}$. The vector $e_j$ has only the $j$-th component non zero, which is $1$. – Vajra Sep 09 '20 at 14:16
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    I would call the vector with the $k$th entry a $1$ and all other entries $0$ the $k$th standard basis (https://en.wikipedia.org/wiki/Standard_basis) vector in $\mathbb{R}^n$, denoted $e_k$. – Clarinetist Sep 09 '20 at 14:35
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    As an aside, you wrote "this is one of the members of the orthonormal base of $\Bbb R^n$." The English article "the" carries with it a connotation that what it describes is the only of its description. There are many orthonormal bases possible for $\Bbb R^n$. The one you are thinking of just happens to be the most standard. – JMoravitz Sep 09 '20 at 15:10

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