The Wikipedia page of this article is basically a masterclass why Wikipedia is useless for learning technical subjects. They are not even able to teach such a simple subject properly there!
Bibliography:
- www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf gives a definition that does not consider upper and lower indexes, it only counts how many times the indices appearTheir definition of the Laplacian is a bit wrong as only one appears in it, they likely meant to have written instead of , related:
Einstein notation, also known as Einstein summation convention, is a notational scheme used primarily in the fields of mathematics and physics to simplify expressions involving tensors and multi-indexed arrays. It was introduced by the physicist Albert Einstein in the context of his work on the theory of relativity. The key principle of Einstein notation is that when an index variable appears twice in a single term, it implies a summation over that index.
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