Let $A$ be a $(p\times p$)-Jordan block of generalized eigenvalue $\lambda$. Let $B$ be a $(q\times q$)-Jordan block of generalized eigenvalue $\mu$. Then what is the Jordan canonical form for $A\otimes B$, where $\otimes$ is the Kronecker product?

I found a reference here without a proof (Horn, Roger A., and Charles R. Johnson. Matrix analysis. Cambridge university press, 1990.):

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I will be appreciated if anyone can give me a proof of part (a).


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