Objects that have both upper and lower indices, reflecting both types of transformation. 3. The Metric Tensor ( gijg sub i j end-sub
It acts as a bridge, allowing you to "lower" a contravariant index to make it covariant, or "raise" it using its inverse ( gijg raised to the i j power Principles of Tensor Calculus: Tensor Calculus
). This process keeps the underlying physical meaning intact while changing the mathematical representation. 4. Covariant Differentiation Objects that have both upper and lower indices,
Tensors are defined by how their components transform during a change of coordinates. There are two primary types of transformation: Contravariant ( Aicap A to the i-th power Principles of Tensor Calculus: Tensor Calculus