What are Tensors?

In mathematics, it is an algebraic object that describes the linear mapping from one set of algebraic objects to another.

• Objects that the tensors may map between include, but are not limited to the vectors, scalars, and recursively, even other tensors (for example, a matrix is a map between vectors and thus a tensor. Therefore the linear map between matrices is also the tensor).

• Tensors are inherently related to vector spaces and their dual spaces and can take several different forms.

• For example, a scalar, a vector, a dual vector at a point, or a multi-linear map between vector spaces.

• Euclidean vectors and scalars are simple tensors. While tensors are defined as independent of any basis.

• The physics literature is often referred to by its components on a basis related to a particular coordinate system.