In multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis. In physics, a basis is sometimes thought of as a set of reference axes.

What is meant by covariant vector?

A covariant vector or cotangent vector (often abbreviated as covector) has components that co-vary with a change of basis. That is, the components must be transformed by the same matrix as the change of basis matrix. The components of covectors (as opposed to those of vectors) are said to be covariant.

What are Contravariant and covariant four vector?

If an object transforms in the same way as basis vectors, its a Covariant vector also called a 1-form. If it transforms as coordinates, and therefore in the opposite direction as basis vectors, it's a Contravariant vector, or just a vector.