What is a tensor? Define contra variant and covariant tensor.
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Another Explanation (5):
A tensor is a multi-dimensional array of numbers that transforms according to specific rules under coordinate transformations.
| Tensor Type | Transformation Rule | Description |
|---|---|---|
| Contravariant Tensor | T'i = ∂x'i/∂xj * Tj | Transforms inversely to the coordinate transformation. Think of vectors representing displacements. |
| Covariant Tensor | T'i = ∂xj/∂x'i * Tj | Transforms in the same way as the coordinate transformation. Think of covectors (or dual vectors) representing linear functionals. |