General Relativity/The Tensor Product

<General Relativity

If $𝐓$ and $𝐒$ are tensors of rank $n$ and $m$, then there exists a tensor $𝐓\otimes 𝐒$ 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 $𝐓=T_{\beta }^{\alpha }$ and $𝐒=S_{\mu \nu },$then $𝐓\otimes 𝐒=T_{\beta }^{\alpha }{S}_{\mu \nu }$.

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...