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?
[Math] Notation for null vector with one entry = 1
linear algebranotation
Best Answer
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 $\ell^p(A)$).