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He folks, here's my problem:

Let $\mathbf{A}, \mathbf{B}, \mathbf{X}_1, \mathbf{X}_2, \mathbf{X}_3, \mathbf{Y}_1, \mathbf{Y}_2, \mathbf{Y}_3\in\mathbb{R}^{3\times 3}$ with determinante det()=+1. The matrices $\mathbf{A}$, $\mathbf{B}$, $\mathbf{X}_1$, $\mathbf{X}_2$ and $\mathbf{X}_3$ are known and the relation

$\mathbf{A}\mathbf{B}=\mathbf{X}_1\mathbf{X}_2\mathbf{X}_3 \mathbf{B}=\mathbf{X}_1 \mathbf{Y}_1 \mathbf{X}_2\mathbf{Y}_2 \mathbf{X}_3\mathbf{Y}_3$

is valid if the matrices $\mathbf{X}_i$ and $\mathbf{Y}_i$ have the same structure.

The question is: How to determine the matrices $\mathbf{Y}_1$, $\mathbf{Y}_2$ and $\mathbf{Y}_3$ such that the matrices $\mathbf{X}_i$ and $\mathbf{Y}_i$ have the same structure and depend on components of $\mathbf{B}$, e.g. $\mathbf{Y}_1(\mathbf{B})$?

I'm grateful for any suggestion.

edit: I have extended my original posting and tried to explain the problem in more detail.

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1 Answer 1

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If $X_1, X_2, X_3$ are invertible, $Y_1$ and $Y_2$ can be any invertible matrices and $Y_3 = (X_1 Y_1 X_2 Y_2 X_3)^{-1} A B$.

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