B alternative notations for the Tucker3 model

In simultaneous components notation the Tucker3 model reads  

Using this notation it is clear that all slabs X are modeled with the same component matrices A and B, but different core-matrices. There are further two fully equivalent ways of writing the Tucker3 model in simultaneous components notation form. 

Using the tensor product notation it becomes clear that the Tucker3 model generalizes the PARAFAC model. Not only tensor products of the same components in all three modes are taken, but also their cross-products. Moreover, the Tucker3 model allows for a different number of components in all three modes. 

In simultaneous components notation the Tucker2 model for the (/ x J x K) array X reads 

The Tuckerl model in Kronecker products notation reads  

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