I know the following relationship holds between the Kronecker product and the vectorization operator ($vec(.)$):
$vec(ABC) = (C^T \otimes A)vec(B)$
A proof for this can be found here: https://www.ime.unicamp.br/~cnaber/Kronecker.pdf
I think the following equality should also be correct:
$vec(ABC) = (A^T \otimes C)vec(B)$
I tried to prove it using the same reasoning, but I couldn't. Any help is appreciated.
Thank you!