- #1

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## Homework Statement

Which (if any) of the following are valid tensor expressions:

(a)[itex]A^\alpha+B_\alpha[/itex]

(b)[itex]R^\alpha{}_\beta A^\beta+B^\alpha=0[/itex]

(c)[itex]R_{\alpha\beta}=T_\gamma[/itex]

(d)[itex]A_{\alpha\beta}=B_{\beta\alpha}[/itex]

## Homework Equations

Nothing relevant - these are generic tensors.

## The Attempt at a Solution

(a) and (c) are not valid because the indices don't match up. (d) is valid - in matrix notation, A=B

^{T}.

I'm not sure about (b), though. The left hand side is valid; summing over the dummy index makes it a sum of two vectors. I'm not quite sure how to interpret the equality, though. I can see it as a vector equaling a scalar - which is not valid. Alternatively, I can read an implicit [itex]\forall \alpha[/itex] - in other words, that each element of the vector on the left hand side is identically zero.

I lean towards the first interpretation - but I'm not sure.