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Subsection 3.1.2 Symmetric and Antisymmetric Tensors

A tensor whose two contravariant or covariant indices can be interchanged without affecting the value of the tensor, then it is called symmetric tensor in these indices. If \(A^{ij} = A^{ji}\) then the tensor is symmetric contravariant tensor in the indices \(i\) and \(j\text{.}\) Again, if \(A^{ij} = -A^{ji}\) then the tensor is called skew symmetric contravariant tensor . The same is true for covariant tensor . The symmetric or antisymmetric is defined for a pair of contravariant or covariant indices. However, the Kronecker delta which is a mixed tensor for one contravariant and covariant indices is symmetric in its indices.