express a matrix using Kronecker product

Question

How to express the following matrix as a Kronecker product of two $2\times 2$ matrices:

\begin{equation*} A = \begin{pmatrix} 0 & 0 & 0 & 1+j \\ 0 & 0 & 1-j& 0 \\ 0 & 1-j & 0& 0\\ 1+j& 0& 0&0 \end{pmatrix} \end{equation*}

Answer 1

I am not sure this is what you were looking for... $$ A = \left(\begin{array}{c c} 0 & 1 \\ 1 & 0 \end{array}\right) \otimes \left(\begin{array}{c c} 0 & 1 \\ 1 & 0 \end{array}\right) + \left(\begin{array}{c c} 0 & 1 \\ -1 & 0 \end{array}\right) \otimes \left(\begin{array}{c c} 0 & j \\ -j & 0 \end{array}\right) $$