Tensors

Overview [1]#

Tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other Tensors.

Elementary examples of such relations include the dot product, the cross product, and linear maps. Geometric vectors, often used in physics and engineering applications, and scalars themselves are also Tensors.

A more sophisticated example is the Cauchy stress tensor T, which takes a direction v as input and produces the stress T(v) on the surface normal to this vector for output, thus expressing a relationship between these two vectors,

Tensors consists of a set of primitive values shaped into an array of any number of dimensions. A tensor's rank is its number of dimensions. Here are some examples of tensors: 

3 # a rank 0 tensor; this is a scalar with shape []
[1. ,2., 3.] # a rank 1 tensor; this is a vector with shape [3]
[[1., 2., 3.], [4., 5., 6.]] # a rank 2 tensor; a matrix with shape [2, 3]
[[[1., 2., 3.]], [[7., 8., 9.]]] # a rank 3 tensor with shape [2, 1, 3]
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