A tensor is something that transform as a tensor. Gtfo Christoffel symbols.
Duck typing ftw
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
It’s all just pointers with semantics attached.
Vectors with strides.
good ol’ nominal typing
Square matrices are linear endomorphisms. They are isomorphic to (1,1) tensors but not any other rank of tensors.
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.
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?)
Everything’s a matrix if u fuck with it hard enough