Fourth Order Tensors in Physics and MechanicsFourth order tensors have also wide applications in physics and mechanics. Examples include the piezo-optical tensor, the elasto-optical tensor and the flexoelectric tensor. The most well-known...doi:10.1007/978-981-10-8058-6_8Qi, Liqun...
In all these examples A⃗ ,A˜,R1,R2A→,A~,R1,R2 are invariant under change of coordinates. As far as I understand A⃗ ϵVA→ϵVA⃗ ∈VA→∈V, A˜ϵV∗A~ϵV∗A˜∈V∗A~∈V∗, R1ϵV∗⊗V⊗V∗R1ϵV∗⊗V⊗V∗R1∈V∗⊗V⊗V∗R1...
• A 2-dimensional tensor is a matrix • A 3-dimensional tensor is like a matrix with an extra dimension etc. AND a tensor usually has all values linked somehow, so the tensor obeys transformation rules such as being able to be rotated or scaled. Examples: • in physics a tenso...
Some examples of skew-symmetric tensors in Physics are illustrated.Rodriguez-Valverde, Miguel Angel; Tirado-Miranda, Mariadoi:10.48550/arXiv.0904.1814Miguel Angel Rodriguez-ValverdeMaria Tirado-Mirandaphysics
In physics, tensor is an object that operates on a vector to produce another vector [44]. In computer science, tensor is an n dimensional array that represents data. The rank or order of a tensor is determined by the number of axes. Tensors can take several different forms depending on ...
In mathematics, tensor is an object that describes the relation between sets of objects related to vector space. In physics, tensor is an object that operates on a vector to produce another vector[44]. In computer science, tensor is an n dimensional array that represents data. The rank or ...
The physics/tensor analysis view of tensors includes behavior under changes of coordinates. You can think of a scalar as a zeroth order tensor, one that behaves as simply as possible under a change of coordinates, i.e. doesn’t change at all. Posted in Math Tagged Math Tensors 2 ...
The documentation is roughly split in two parts: on one hand the full "reference" containing the documentation of all functions, classes, methods, etc., and on the other hand the "user guide" containing some introductions with additional explanations and examples. The documentation is based on ...
cuda.DoubleTensor] dims = [1, 2, 3] for dtype, dim in itertools.product(dtypes, dims): torch.manual_seed(1234) tensor = torch.FloatTensor(*([17] * dim)).random_(-100, 100) tensor = tensor.type(dtype) tensor = torch.autograd.Variable(tensor, requires_grad=True) summed = hvd.all...
Every scalar is an isotropic tensor of zeroth order, while the unit tensor and the permutation tensors are examples of isotropic tensors of second and third order. There are no isotropic tensors of first order, i.e., vectors. All spherical second-order tensors are isotropic. Likewise, a ...