The difference between a matrix and a 2d array of numbers is the operations that are performed
A tensor really isn't standardized in the same way so it's basically just an n-d array in my mind
40It's all just pointers with semantics attached.
29Vectors with strides.
8
You can force a 2D array to be a matrix if you're clever enough
3good ol' nominal typing
2Well, it would still be a vector. So some standardisation.
2
A tensor is something that transform as a tensor. Gtfo Christoffel symbols.
15Duck typing ftw
6
How you describe a thing is different from what a thing is... A tensor is not a matrix.
And on mathematics, "what a thing is" is a completely useless concept... So, it makes no difference whatsoever.
13the "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?)
0
Square matrices are linear endomorphisms. They are isomorphic to (1,1) tensors but not any other rank of tensors.
7a 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.)
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