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- Dirac says that a general rank-2 tensor ## T^{\mu\nu} ## can be decomposed as ## A^\mu B^\nu + A'^\mu B'^\nu + A''^\mu B''^\nu + \cdots\, ##. Is this obvious?

Dirac's book "General Theory of Relativity" says on p. 2 that a general rank-2 tensor can be written as a sum of outer products: $$ T^{\mu\nu} = A^\mu B^\nu + A'^\mu B'^\nu + A''^\mu B''^\nu + \cdots $$ Importantly, he repeats this on p. 18, in developing the covariant derivative, where he mentions that a tensor ## T_{\mu\nu} ## is "expressible as a sum of terms like ## A_\mu B_\nu ##".

Is this obvious? Can someone show or explain this?

Is this obvious? Can someone show or explain this?

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