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i want to solve the following equation. $\begin{bmatrix} \mathbf{A_1} & \mathbf{A_2} & \mathbf{A_3} & \mathbf{A_4} \\ \mathbf{A_5} & \mathbf{A_6} & \mathbf{A_7} & \mathbf{A_8} \end{bmatrix} \begin{bmatrix} \mathbf{w_1} \\ \mathbf{w_2} \\ \mathbf{w_3} \\ \mathbf{w_4}\end{bmatrix} = \mathbf{0}$ say Equation (1)

where $\mathbf{A}_i = \mathbf{B}_i \otimes \mathbf{D}_i$. Here, $\mathbf{B}_i$ and $\mathbf{D}_i$ are matrice of size 2 x 2 with non-zero elements and full rank. These matrices are given.

$\mathbf{w}_i = \mathbf{x}_i \otimes \mathbf{y}_i$. Here, $\mathbf{x}_i$ and $\mathbf{y}_i$ are vectors of size 2 x 1 and are variables. How to find the vectors $\mathbf{x}_i$ and $\mathbf{y}_i$?

Note: I calculated the solution space of the $\mathbf{w}$ vectors by calculating the null space of the matrix. i took one vector from the solution space and tried to find $\mathbf{x}_i$ and $\mathbf{y}_i$ from $\mathbf{w}_i$ but it didnot satisfy $\mathbf{w}_i = \mathbf{x}_i \otimes \mathbf{y}_i$.

Thank you in advance

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    Your matrix is $8\times 16$ and therefore the nullspace is at least 8 dimensional but there is no guarantee that the overall rank is not less than 8. Did you check the overall rank? How did you calculate the $x_i$'s and $y_i$'s?2011-09-16
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    i checked the rank of 8 x 16 matrix, it is 8 and hence the null space is of rank 8.2011-09-16
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    i checked the rank of 8 x 16 matrix, it is 8 and hence the null space is of rank 8. i took $\mathbf{w}_1$ and and reversed the kronecker operation. That is i took the four elements of $\mathbf{w}_1$ and divided the first two elements with the third and fourth elements, element wise to check if both division results in a constant. I thinks kronecker produce is not uniquely reversible but to a scaling factor.2011-09-16
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    let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/1361/discussion-between-karthik-and-percusse)2011-09-16

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