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What Is a Tensor? The mathematical point of view. - Physics Forums 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 The tensor product of elements in these vector spaces that one usually sees in engineering and physics texts (frequently matrices) is basically an element in the tensor product of the corresponding vector spaces
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)
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
Difference Between Tensor and Tensor field? - Mathematics Stack Exchange A scalar is a tensor of order or rank zero , and a scalar field is a tensor field of order zero A vector is a tensor of order or rank one , and a vector field is a tensor field of order one Some additional mathematical details Rn R n is a vector space representing the n-tuples of reals under component-wise addition and scalar multiplication
Is Tensor Quantity a Combination of Vector and Scalar? A tensor works is just a generalization of the vector concept (in fact a vector is a rank 1 tensor, and even a scalar can be considered a rank 0 tensor!) Suppose I write down a matrix on a piece of paper and tell you that it represents the moment of inertia of some object Then I tell you to transform it into a more convenient coordinate system