What Is a Tensor? The mathematical point of view. A tensor itself is a linear combination of let’s say generic tensors of the form In the case of one doesn’t speak of tensors, but of vectors instead, although strictly speaking they would be called monads
What, Exactly, Is a Tensor? - Mathematics Stack Exchange Every tensor is associated with a linear map that produces a scalar For instance, a vector can be identified with a map that takes in another vector (in the presence of an inner product) and produces a scalar
What even is a tensor? - Mathematics Stack Exchange We call that an operator is (n, m) tensor (or tensor field) if it is a linear operators that takes m vectors and gives n vectors Conventionally, 0 -vectors is just a scalar
How would you explain a tensor to a computer scientist? A tensor extends the notion of a matrix analogous to how a vector extends the notion of a scalar and a matrix extends the notion of a vector A tensor can have any number of dimensions, each with its own size A $3$ -dimensional tensor can be visualized as a stack of matrices, or a cuboid of numbers having any width, length, and height
How do you transpose tensors? - Mathematics Stack Exchange I don't think I've ever seen a transpose defined for 3D arrays What does your matrix represent? Can you provide more context for your question? Does the matrix represent a linear transformation of some kind, or is it just a container for data?
Tensor-Hom adjunctions - Mathematics Stack Exchange It turns out the two bimodules you mention are isomorphic Adjunction in general gives you the bijection you described However, in the proof of the Hom Tensor adjunction, the map that you define for the bijection can be seen to also be a homomorphism Really you have to write out the proof in detail, and observe that you are dealing with homomorphisms More information can be found here