Write up the transformation laws of the tensors: \( A^i_{jk} \) and \( B^m_{ijk} \\), and \( C^m \).
JU-PHY2nd YearFinalMathematical PhysicsTensor AnalysisContra variant and covariant tensors (Topic Practice)JU-PHY - ⚡ অনলাইন প্রশ্নব্যাংক দেখুন 💥
Another Explanation (5): ```html
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| Tensor | Transformation Law |
|---|---|
| \(A^i_{jk}\) | \( \bar{A}^i_{jk} = \frac{\partial \bar{x}^i}{\partial x^p} \frac{\partial x^q}{\partial \bar{x}^j} \frac{\partial x^r}{\partial \bar{x}^k} A^p_{qr} \) |
| \(B^m_{ijk}\) | \( \bar{B}^m_{ijk} = \frac{\partial \bar{x}^m}{\partial x^n} \frac{\partial x^p}{\partial \bar{x}^i} \frac{\partial x^q}{\partial \bar{x}^j} \frac{\partial x^r}{\partial \bar{x}^k} B^n_{pqr} \) |
| \(C^m\) | \( \bar{C}^m = \frac{\partial \bar{x}^m}{\partial x^n} C^n \) |