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Raised and lowered indices

Ciro Santilli (@cirosantilli, 37) ... Mathematics Area of mathematics Algebra Linear algebra Tensor Einstein notation
Updated 2025-07-16  0 By others on same topic  0 Discussions Create my own version
TODO what is the point of them? Why not just sum over every index that appears twice, regardless of where it is, as mentioned at: www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf.
Vectors with the index on top such as xi are the "regular vectors", they are called covariant vectors.
Those in indices on bottom are called contravariant vectors.
It is possible to change between them by Raising and lowering indices.
The values are different only when the metric signature matrix is different from the identity matrix.
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    • Raised index Raised and lowered indices
    • Lowered index Raised and lowered indices
    • Raising and lowering indices Raised and lowered indices

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Raised and lowered indices

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Raised and lowered indices

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