How to denote a one-hot vector space, like $\mathbb{R}^n$ but for one-hot vectors?

Question

For real vector $v_r$ we can write $v_r \in \mathbb{R}^n$.

For binary vector $v_b$, I think we can write $v_b \in \{0,1\}^n$.

But how should we write a one-hot vector $v_i$?

Answer 1

You could denote the set of one-hot vectors by:

$$ \left\{ v \in \{0,1\}^n : \sum \limits_{i=1}^n v_i = 1 \right\} $$