Symmetric tensor

A symmetric tensor is unchanged by every permutation of its slots. A symmetric second-rank tensor is the rank-two case; symmetry for higher rank requires invariance under every such slot exchange.

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- Symmetric second-rank tensor Symmetric tensor

Symmetric second-rank tensor ( $T_{ij} = T_{ji}$ )

A second-rank tensor is symmetric when

T_{ij} = T_{ji}

. Every second-rank tensor has the unique decomposition

T_{ij} = \frac{T _{ij} + T _{ji}}{2} + \frac{T _{ij} - T _{ji}}{2}

into symmetric and antisymmetric parts.

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Massive spin-two field

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