Search results
Results from the WOW.Com Content Network
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.
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 (−,+,+,+).
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 ...
For compactness and convenience, the Ricci calculus incorporates Einstein notation, which implies summation over indices repeated within a term and universal quantification over free indices. Expressions in the notation of the Ricci calculus may generally be interpreted as a set of simultaneous equations relating the components as functions ...
Nikki Glaser delivered a number of mic drop moments at the 2025 Golden Globes — from the red carpet to the stage!. Ahead of her hosting duties, the stand-up comedian made her mark in a gold silk ...
The Casimir invariants of the Poincaré group are = , (Einstein notation) where P is the 4-momentum operator, and = , where W is the Pauli–Lubanski pseudovector. The eigenvalues of these operators serve to label the representations.