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Implicit metric signature in Einstein notation

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
Then a specific metric is involved, sometimes we want to automatically add it to products.
E.g., in a context considering the common Minkowski inner product matrix where the η 4x4 matrix and μ is a vector in R4
xμxμ​=xμημν​xν=−x02​+x12​+x22​+x32​;
(1)
which leads to the change of sign of some terms.

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