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  [[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]