$n$th-order Hadamard power (or root) of a vector

Question

I am familiar with the notation of the $n$th-order Hadamard power $$ \mathbf{A}^{\circ n} $$ or root $$ \mathbf{A}^{\circ \frac{1}{n}} $$

I wonder if it is sensible to use this notation for vectors as well, that is, $$ \mathbf{v}^{\circ n} = (v_1^n, v_2^n, \dots, v_N^n) $$ and $$ \mathbf{v}^{\circ \frac{1}{n}} = \left(\sqrt[n]{v_1}, \sqrt[n]{v_2}, \dots, \sqrt[n]{v_N}\right) $$

Answer 1

Of course, since your (row) vector $$\mathbf v= (v_1,v_2,\dots, v_N)$$ is nothing more than a particular case of a matrix $A$ (with one row and $N$ columns).

Hadamard product, which you are "familiar with", deals with matrices (not linear transformations ;-) ), in particular with row or column matrices.