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  • Tensors Explained: Scalars, Vectors, Matrices Math
    Tensor Product Properties Definition: A tensor product of vector spaces is a vector space structure on the Cartesian product that satisfies This means a tensor product is a freely generated vector space of all pairs that satisfies some additional conditions such as linearity in each argument, i e bilinearity, which justifies the name product
  • 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
  • Trace of tensor product vs Tensor contraction - Mathematics Stack Exchange
    The Wiki page "Tensor Contraction" speaks of tensor contraction as some generalization of trace, though without providing any formulation or example My questions: How do they all work?
  • How does one calculate the Tensor product of two matricies?
    One participant expresses confusion about the tensor product of the identity matrix with another matrix and seeks clarification on how to derive the resulting matrix intuitively Another participant corrects a misunderstanding regarding the nature of the basis elements involved in the tensor product calculation
  • 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
  • Is current truly a scalar quantity or a tensor? - Physics Forums
    The discussion revolves around the nature of electric current, specifically whether it should be classified as a scalar quantity or a tensor Participants explore concepts related to current density, the behavior of charge carriers, and the implications of treating current as a vector or tensor in different contexts, including circuit theory and continuum models Some participants suggest that
  • 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
  • ##\mathbb {C}\oplus\mathbb {C}\cong\mathbb {C}\otimes\mathbb {C . . .
    Discussion Overview The discussion revolves around the isomorphism between the algebraic structures C ⊕ C and C ⊗ R C Participants explore the nature of this isomorphism, the mappings involved, and the implications of tensor products in the context of complex algebras Discussion Character Debate contested Technical explanation Mathematical reasoning Main Points Raised One participant
  • tensor rotation - Mathematics Stack Exchange
    You are considering the transformation law of the tensors and this depends on the nature of the tensor Vectors transform in a certain way and other objects transform in other ways
  • What is a Rank 3 Tensor and Why Does It Matter? - Physics Forums
    A rank 3 tensor inputs three generalized vectors (i e either a vector or their dual vector), and spits out a scalar One can also think of it as inputting 2 generalized vectors (or a rank 2 tensor), and outputting a vector, or inputting 1 generalized vector, and outputing 2 vectors (or a rank 2 tensor)





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