express a matrix using Kronecker product 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*}

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