Define a tensor. What do you understand by contravariant and covariant tensors?
JU-PHY2nd YearFinalMathematical PhysicsTensor AnalysisContra variant and covariant tensors (Topic Practice)JU-PHY - ⚡ অনলাইন প্রশ্নব্যাংক দেখুন 💥
Another Explanation (5): A tensor is a generalization of scalars, vectors, and matrices to higher dimensions. It can be thought of as a multi-dimensional array of numbers that transforms according to specific rules under coordinate transformations.
Contravariant tensors transform in the *same way* as the basis vectors change. Their components scale *inversely* to the coordinate transformation. Vectors are examples of contravariant tensors of rank 1.
Covariant tensors transform in the *same way* as the dual basis vectors (one-forms) change. Their components scale in the *same way* as the coordinate transformation. One-forms (linear functionals) are examples of covariant tensors of rank 1.