High Quality Content by WIKIPEDIA articles! 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. For holonomic bases, this is determined by a change from one coordinate system to another. When an orthogonal basis is rotated into another orthogonal basis, the distinction between co- and contravariance is invisible. However, when considering more general coordinate systems such as skew coordinates, curvilinear coordinates, and coordinate systems on differentiable manifolds, the distinction is significant.