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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
An Introduction to Tensors - Mathematics Stack Exchange In mathematics, tensors are one of the first objects encountered which cannot be fully understood without their accompanying universal mapping property Before talking about tensors, one needs to talk about the tensor product of vector spaces You are probably already familiar with the direct sum of vector spaces This is an addition operation on spaces The tensor product provides a
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 exactly is a tensor product? - Mathematics Stack Exchange This is a beginner's question on what exactly is a tensor product, in laymen's term, for a beginner who has just learned basic group theory and basic ring theory I do understand from wikipedia th
Tensor-Hom adjunctions - Mathematics Stack Exchange 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
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
What even is a tensor? - Mathematics Stack Exchange I'm an electrical engineer, and thus don't often interact with the types of mathematics that involve tensors But when I try to get a deeper understanding of certain things that I do interact with, I