What is a tensor?

This definition is often used to describe tensors on manifolds, and readily generalizes to other groups. A downside to the definition of a tensor using the multidimensional array approach is that it is not apparent from the definition that the defined object is indeed basis independent, as is expected from an intrinsically geometric object.

What is an example of a 2nd order tensor?

For example, in a fixed basis, a standard linear map that maps a vector to a vector, is represented by a matrix (a 2-dimensional array), and therefore is a 2nd-order tensor. A simple vector can be represented as a 1-dimensional array, and is therefore a 1st-order tensor.

What is the history of tensor analysis?

In the 20th century, the subject came to be known as tensor analysis, and achieved broader acceptance with the introduction of Einstein ‘s theory of general relativity, around 1915. General relativity is formulated completely in the language of tensors.

What is a tensor of Type (P/Q) called?

A tensor of type (p, q) is also called a (p, q) -tensor for short. This discussion motivates the following formal definition: Definition. A tensor of type ( p, q) is an assignment of a multidimensional array