Is there a common notation for a vector which has all elements equal to 0 except for one, which is equal to 1? I was considering using a Kronecker delta, but the standard use of two subscripts, $\delta_{ij}$, seems unnecessary since it is a vector and therefore a rank 1 tensor, whereas the two indices suggest a rank 2 tensor. Any thoughts?

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    $\begingroup$ Fairly common is $e_i$. $\endgroup$ – Daniel Fischer Sep 18 '13 at 22:12
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    $\begingroup$ And the components of $e_i$ are in fact $\delta_{ij}$. $\endgroup$ – mrf Sep 18 '13 at 22:14
  • $\begingroup$ @DanielFischer: If you submit your comment as an answer I would be glad to accept it. $\endgroup$ – okj Sep 18 '13 at 22:44

A common notation (the most common, as far as I am aware) for a vector with one component $1$ and all other components $0$ is $e_i$, where the $1$ is in the $i$-th place. This notation is not only common for vectors in $F^n$, where $F$ is a field, also in sequence spaces ($\ell^p$ etc.) and products $F^A$ where $A$ is an uncountable index set, and subspaces thereof (like $\ell^p(A)$).


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