First matrix is a Kronecker product. Second is not. Can it be wriyten as a Kronecker product?

Question

Can somebody please tell how can I write the matrix system [ b11 b12 0 0; b21 b22 0 0; 0 0 b11 b12; 0 0 b21 b22][u11 u21 u12 u22] into [b11 b12 0 0; 0 0 b11 b12; b21 b22 0 0; 0 0 b21 b22][u11 u12 u21 u22]? Actually I am getting the second matrix but Iwant to get first system. Is there any way to convert the second system into first?

Answer 1

It seems as though you want to "write" the matrix product $$ \left(\begin{array}{cccc} b_{11} & b_{12} & 0 & 0\\ 0 & 0 & b_{11} & b_{12}\\ b_{21} & b_{22} & 0 & 0\\ 0 & 0 & b_{21} & b_{22} \end{array}\right) \pmatrix{u_{11}\\ u_{12}\\ u_{21}\\ u_{22}} $$ in a different way, but you don't clarify exactly what you mean by that. If we switch the second row and third row, then we have $$ \left(\begin{array}{cccc} b_{11} & b_{12} & 0 & 0\\ b_{21} & b_{22} & 0 & 0\\ 0 & 0 & b_{11} & b_{12}\\ 0 & 0 & b_{21} & b_{22} \end{array}\right) \pmatrix{u_{11}\\ u_{12}\\ u_{21}\\ u_{22}}. $$ Perhaps this is what you wanted.