Is Levi-Civita a tensor?
[edit] Is the Levi-Civita symbol a tensor? In the physicist’s conception, a tensor is characterized by its behavior under transformations between bases of a certain underlying linear space. If the most general basis transformations are considered, the answer is no, the Levi-Civita symbol is not a tensor.
Is the Levi-Civita symbol a tensor?
How does Levi-Civita tensor transform?
Under a general coordinate change, the components of the permutation tensor are multiplied by the Jacobian of the transformation matrix. This implies that in coordinate frames different from the one in which the tensor was defined, its components can differ from those of the Levi-Civita symbol by an overall factor.
What is symmetric and antisymmetric tensor?
Antisymmetric and symmetric tensors A tensor A that is antisymmetric on indices and has the property that the contraction with a tensor B that is symmetric on indices and. is identically 0.
What do you mean by symmetric tensor?
In mathematics, a symmetric tensor is a tensor that is invariant under a permutation of its vector arguments: for every permutation σ of the symbols {1, 2., r}. Alternatively, a symmetric tensor of order r represented in coordinates as a quantity with r indices satisfies.