Is the Kronecker sum
$ A \oplus B = A \otimes I_b + I_a \otimes B$
an affine function?
Also, if so, would the following function also be an affine transformation
$f(A,B) := A \otimes M_1 + M_2 \otimes B$
for any positive-definite matrices $M_1$ and $M_2$?