A tensor is an algebraic object that describes a (multilinear)
relationship between sets of algebraic objects related to a vector
space. Objects that tensors may map between include vectors (which
are often, but not always, understood as arrows with length that
point in a direction) and scalars (which are often familiar numbers
such as the real numbers), and, recursively, even other tensors.
Tensors are defined independent of any basis, although they are often
referred to by their components in a basis related to a particular
The shape of tensor (the number of dimensions and the size of each dimension)
might be only partially known.
The rank of tensor, i.e.
The rank of tensor, i.e. the number of dimensions.
The shape of tensor, i.e the size of each dimension.