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 $M_2$?

  • $\begingroup$ What does it mean for a function of two arguments to be affine? Are you asking if the sum is affine with respect to each input? $\endgroup$ – Omnomnomnom Oct 8 '18 at 21:49
  • $\begingroup$ I'm treating (A,B) as a vector, so asking if it is affine with respect to all the elements of both A and B. $\endgroup$ – Betterthan Kwora Oct 8 '18 at 23:13

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