Principles Of Tensor Calculus: Tensor Calculus -

Tensor calculus allows us to write "coordinate-free" laws. Instead of writing separate equations for

Contraction is the process of summing over a repeated upper and lower index (Einstein summation convention). This reduces the "rank" of a tensor. For example, contracting a vector with a covector results in a , which is a single value that everyone—regardless of their coordinate system—will agree upon. Summary of Utility Principles of Tensor Calculus: Tensor Calculus

): These are "correction factors" that account for the changing geometry. Tensor calculus allows us to write "coordinate-free" laws