Table of Contents
What is tensor transformation?
Tensors are defined by their transformation properties under coordinate change. One distinguishes covariant and contravariant indexes. Number of indexes is tensor’s rank, scalar and vector quantities are particular case of tensors of rank zero and one. Consider coordinate change .
How do you know if something is a tensor?
If it transform like vectors do, it’s a vector. If it transforms like tensor do, it’s a tensor. The way it transforms will tell you the rank of the tensor, or maybe that it’s neither a vector not a tensor.
What tensor means?
Tensors are simply mathematical objects that can be used to describe physical properties, just like scalars and vectors. In fact tensors are merely a generalisation of scalars and vectors; a scalar is a zero rank tensor, and a vector is a first rank tensor.
What is Torch cat?
torch. cat (tensors, dim=0, *, out=None) → Tensor. Concatenates the given sequence of seq tensors in the given dimension. All tensors must either have the same shape (except in the concatenating dimension) or be empty. torch.cat() can be seen as an inverse operation for torch.
How do you know if something is a tensor PyTorch?
Returns True if obj is a PyTorch tensor. Note that this function is simply doing isinstance(obj, Tensor) . Using that isinstance check is better for typechecking with mypy, and more explicit – so it’s recommended to use that instead of is_tensor .
What is a tensor in physics?
8 Answers. A tensor is a multilinear function that takes as input a collection of vectors, and outputs a scalar. By multilinear, it is meant that the function is linear in each input independently. You can imagine multilinear functions as a local approximations to nonlinear functions that depend on several variables,…
What is the tensor of a vector component?
If a vector is Vi where i runs from 1-3 (or 1-4, or from whatever to whatever), the tensor is Tij, where the first index labels the vector, and the second index labels the vector component (or vice versa). When you rotate coordinates T transforms as
What is the tensor of inertia?
The tensor of inertia: For rotational motion of rigid object, the angular velocity is a vector and the angular momentum is a vector which is a linear function of the angular velocity. The linear map between them is called the tensor of inertia.
What are differential forms of tensors?
Differential forms: these are antisymmetric tensors of rank n, meaning tensors which have the property that Aij = − Aji and the analogous thing for higher rank, where you get a minus sign for each transposition.