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 …

Feb 5, 2015 · Tensor : Multidimensional array :: Linear transformation : Matrix. The short of it is, tensors and multidimensional arrays are different types of object; the first is a type of function, …

Jun 5, 2013 · The components of a rank-2 tensor can be written in a matrix. The tensor is not that matrix, because different types of tensors can correspond to the same matrix. The differences …

Mar 23, 2014 · 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 …

tensor - In new latin tensor means "that which stretches". The mathematical object is so named because an early application of tensors was the study of materials stretching under tension.

Sep 7, 2021 · Also what is the meaning of that comma in the index for the tensor - it is not anywhere included in the definition of $T$. An explanation of how to generally find the …

Jul 7, 2016 · And one more terminology issues worth mentioning here is that a the tensor product of two different vector spaces is sometimes called a tensor product space, but this is usually …

Mar 30, 2015 · In General, the determinant for a rank $ (0,\gamma)$ covariant tensor of order $\Omega$ follows the following convention. In order to preserve covariance, the Levi-Civita …

Jul 31, 2014 · Regarding why a $ (0,1)$ tensor can be considered a vector, that is because (for finite-dimensional vector spaces) any vector space is isomorphic to its double dual vector …

A tensor field has to do with the notion of a tensor varying from point to point . A scalar is a tensor of order or rank zero , and a scalar field is a tensor field of order zero .