Define covariant and contra variant tensors.
A.
B.
C.
D.
JU-PHY2nd YearFinalMathematical PhysicsTensor AnalysisContra variant and covariant tensors (Topic Practice)JU-PHY - ⚡ অনলাইন প্রশ্নব্যাংক দেখুন 💥
Another Explanation (5):
| Tensor Type | Transformation Behavior |
|---|---|
| Covariant | Transforms like the basis vectors: \(T'_{i} = \frac{\partial x^j}{\partial x'^i} T_j\) |
| Contravariant | Transforms like the coordinates: \(T'^i = \frac{\partial x'^i}{\partial x^j} T^j\) |
Related Questions (Any University/Year)
- Define the terms: contravariant, covariant vectors and tensors.
- What do you mean by contraveriant and covariant tensors.
- Find the components of vectors in polar coordinates when their components in Cartesian coordinates are \\( x, y \\) and \\( \\dot{x}, \\dot{y} \\) respectively.
- Define covariant and contravariant tensors.
- What is a tensor? Define contra variant and covariant tensor.
- Define contravariant and co-variant tensors.
- A covariant tensor has components of \\(xy\\), \\(2y-z^2\\) and \\(xz\\) in rectangular coordinates. Find its covariant components in spherical polar coordinates.
- Write up the transformation laws of the tensors: \( A^i_{jk} \) and \( B^m_{ijk} \\), and \( C^m \).
- If \( \bar{A}^p = \frac{\partial \bar{x}^p}{\partial x^q} A^q \) prove that \( A^q = \frac{\partial x^q}{\partial \bar{x}^p} \bar{A}^p \).
- Express in matrix notation the transformation equations for a (i) covariant vector and (ii) a contravariant tensor of rank two, assuming \(N = 3\).
- Write down the transformation laws of the tensors: \\(A_{ijk}^i\\), \\(B_{ijk}^{mn}\\) and \\(C^m\\).
- Define covariant and contravariant tensor.
- Define a tensor. What do you understand by contravariant and covariant tensors?
- A covariant tensor has components \\( xy \\), \\( 2y - z^2 \\), and \\( xz \\) in rectangular coordinates. Find its covariant components in spherical polar coordinates.
- What is a tensor ? Define contra variant and covariant tensors.
- Define the terms: contravariant, covariant vectors and tensors.
- Define covariant and contra variant tensors.