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In mathematics, especially the usage of linear algebra in mathematical physics and differential geometry, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving brevity.
In Einstein notation (implicit summation over repeated index), contravariant components are denoted with upper indices as in = A covector or cotangent vector has components that co-vary with a change of basis in the corresponding (initial) vector space. That is, the components must be transformed by the same matrix as the change of basis matrix ...
In index-free tensor notation, the Levi-Civita symbol is replaced by the concept of the Hodge dual. [citation needed] Summation symbols can be eliminated by using Einstein notation, where an index repeated between two or more terms indicates summation over that index. For example,
Albert Einstein, in 1916, introduced Einstein notation, which summed over a set of indexed terms in a formula, thus exerting notational brevity. For example, for indices ranging over the set {1, 2, 3}, = = = + + is reduced by convention to:
In abstract index notation, the EFE reads as follows: + = where is the Einstein tensor, is the cosmological constant, is the metric tensor, is the speed of light in vacuum and is the gravitational constant, which comes from Newton's law of universal gravitation.
A letter written by Albert Einstein in which he writes out his famous E = mc2 equation has sold at auction for more than $1.2 million, about three times more than it was expected to get, Boston ...
Einstein notation is used throughout this article. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise.
The list is full of examples of this art style and movement that were created by artists from all around the world. So, check them out; maybe it will convince you to become a surrealism enthusiast ...