General Relativity/The Tensor Product

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<General Relativity

If \mathbf{T} and \mathbf{S} are tensors of rank n and m, then there exists a tensor \mathbf{T} \otimes \mathbf{S} of rank n+m. The components of the new tensor (pronounced "T tensor S") are obtained by multiplying the components of the old tensors. In other words, if \mathbf{T} = T^{\alpha}_{\ \beta} and \mathbf{S}=S_{\mu \nu}, then \mathbf{T} \otimes \mathbf{S} = T^{\alpha}_{\ \beta} S_{\mu \nu}.

For example, if T and S are two contravariant, one-rank tensors, then their tensor product is a two-rank, contravariant tensor.

More to come...