In tensor calculations, in a four dimensional space-time, can we make a vector using the diagonal components of a second rank tensor 📷 and say 📷 is a vector ?
No. Tensors transform as tensors, vectors as vectors. The individual components don't have any particular meaning, precisely because they aren't invariant under linear transformations, that act on the tensor and the vector as a whole.
There's no fundamental difference between spacetime (a Lorentzian manifold) and R4, apart from the signature. The question is the same, whether it's about rotations, translations or boosts.
I agree with Stam: look at the transformation of a vector (x1,...,x4) and of a tensor diag(a11,...,a44).
Dear Sadegh Mousavi
You may get a new approach of tensors in geometric Algebra
many thanks for answers, what about third rank tensor?
can we define a vector using some components of a third rank tensor?
Dear Stam and Peter, please pay attention that, we can simply obtain a vector from a third rank tensor using contraction of the third rank tensor. what do you think about this?
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