What are Contravariant and Covariant Components of a Vector?
The contravariant and covariant componets of a vector is central concept of differential geometry. Here we discuss why they are useful and necessary to extend the concept of the length of a vector to a large class of coordinate systems. An example coordinate system having oblique axes is analyzed and explicit formulas for the contravariant and covariant components are found. This provides a foundation for understanding tensors and the metric tensor in higher dimensions.
