I am reading some notes about tensor product of vector spaces (those in here) where the following sentence can be found:
Note that not every matrix on V ⊗ W can be written as a tensor product of a matrix on V and another on W.
Matrices in V ⊗ W are defined as a Kronecker product. So, how could this claim be possible? Has it to do with the problem of splitting the Kronecker product of two matrices?
More generally: does the general picture changes if we consider V and W infinite-dimensional vector spaces?