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I knew how to compute the Kronecker product of two matrices, and maybe use it as a convenient way to vectorize MATLAB code, but I never really understand this operation intuitively.

Can someone point me to some interesting application of Kronecker product, hopefully not on 0-1 matrices?

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This can be easily found with a google search here

https://www.hindawi.com/journals/jam/2013/296185/

On a more personal note, quantum mechanics uses such products quite frequently.

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