What is a tensor ? Define contra variant and covariant tensors.
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Another Explanation (5):
A tensor is a generalization of vectors and matrices to multiple dimensions. It can be thought of as a multi-dimensional array of numbers that transforms in a specific way under coordinate transformations.
| Tensor Type | Transformation Behavior | Description |
|---|---|---|
| Contravariant Tensor | Transforms inversely to the coordinate transformation | Components scale *opposite* to the coordinate change. Think of vectors – their components change in the opposite way to a change of basis. |
| Covariant Tensor | Transforms in the same way as the coordinate transformation | Components scale in the *same* way as the coordinate change. Think of dual vectors (or covectors) or gradients – their components change in the same way as a change of basis. |