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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.
Einstein notation is used throughout this article. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise.
The text here uses Einstein notation in which summation over repeated indices is assumed. Two types of derivatives are used: Partial derivatives are denoted either by the operator ∂ i {\displaystyle \partial _{i}} or by subscripts preceded by a comma.
This section uses Einstein notation, including Einstein summation convention. See also Ricci calculus for a summary of tensor index notations, and raising and lowering indices for definition of superscript and subscript indices, and how to switch between them. The Minkowski metric tensor η here has metric signature (+ − − −).
The equation for the mass shell is also often written in terms of the four-momentum; in Einstein notation with metric signature (+,−,−,−) and units where the speed of light =, as =. In the literature, one may also encounter p μ p μ = − m 0 2 {\displaystyle p^{\mu }p_{\mu }=-m_{0}^{2}} if the metric signature used is (−,+,+,+).
A litter of two-week old puppies was crammed into a bucket and abandoned alongside a road in Union County, New Jersey on Thursday, police said. The nine puppies were found...
In Einstein's theory of general relativity, the Schwarzschild metric (also Schwarzschild vacuum or Schwarzschild solution), is a solution to the Einstein field equations which describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, the angular momentum of the mass, and the universal ...
(The Center Square) – An ongoing war in Syria has suddenly ended with the overturning of the long-standing Syrian government, creating national security and humanitarian concerns but also ...