In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity. It was introduced by Albert Einstein in 1916.
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... In Einstein notation, the usual element reference for the mth row and nth column of matrix A becomes ... We can then write the following operations in Einstein notation as follows ...
... mechanics Electromagnetism Transport phenomena General relativity Computer vision Notation Index notation Multi-index notation Einstein notation Ricci calculus Penrose graphical ... In Einstein notation, contravariant components are denoted with upper indices as in For a dual vector (also called a covector) to be basis-independent, the components of the dual vector must ... In Einstein notation, covariant components are denoted with lower indices as in In physics, vectors often have units of distance or distance times some other unit (such as the velocity ...
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“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.”
—Albert Einstein (18791955)