It's all just pointers with semantics attached.

You can force a 2D array to be a matrix if you're clever enough

good ol' nominal typing

Well, it would still be a vector. So some standardisation.

Everything's a matrix if you realize there is no spoon

Duck typing ftw

the "categorical" way of defining tensor products is essentially "that thing that lets you turn multi-linear maps into linear maps", and linear maps (of finite dimensional vector spaces) are basically matrices anyways. so i don't see it as much of a stretch to say tensors are matrices.

(can you tell that i never took a physics class?)

a tensor is a multi-linear map V × ... × V × V^^ × ... × V^^ → F, and a multi-linear map V × ... × V × V^^ × ... × V^^ → F is the same as a linear map V ⊗ ... ⊗ V ⊗ V^^ ⊗ ... ⊗ V^^ → F. and a linear map is ""the same thing as"" a matrix. so in this way, you can associate matrices to tensors. (but the matrices are formed in the tensor space V ⊗ ... ⊗ V ⊗ V^^ ⊗ ... ⊗ V^^, not in the vector space V.)