Multiplication of kronecker products is reversed

[apmypb]

It seems that the product $(A_1 \otimes B_1) \cdot \dots\cdot (A_n \otimes B_n)$ is falsely computed as
$(A_n\cdot\dots\cdot A_1) \otimes (B_n\cdot\dots\cdot B_1)$ and not like $(A_1\cdot\dots\cdot A_n) \otimes (B_1\cdot\dots\cdot B_n)$ (the order of maps reversed)
One can check the following minimal working example:

using LinearAlgebra
using LinearMaps

A = [0 1; 0 0]
B = [0 0; 1 0]
J = LinearMap(I, 1)
Matrix(kron(J, A*B)) == Matrix(kron(J, A) * kron(J, B)) # should be true

Applying reverse() on the tuples before the product should do the trick

LinearMaps.jl/src/kronecker.jl

Line 275 in ee91b4f

_unsafe_mul!(y, kron(prod(As), prod(Bs)), x)

[dkarrasch]

Thanks for catching this! It had a test, which used the same linear maps, so didn't see the missing reverse. 🤦