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Let $A\in\mathbb{R}^{9\times 9}$, and $I_3\in\mathbb{R}^{3\times 3}$ is the identity matrix. Now I am going to find a matrix $\Lambda\in\mathbb{R}^{3\times 3}$ and $x\in\mathbb{R}^9$ such that $$(A-\Lambda\otimes I) x=0$$ where $\otimes$ is the Kronecker product. It looks like a generalized eigenvalue problem compared to the regular one $(A-\lambda I)x=0$. Has anyone ever seen this kind of problem?

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