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(also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed terms...

matrix, and in the rightmost expression the summation sign was suppressed: this is the Einstein summation convention, which will be used throughout this article...

products of scalar components of the tensor(s) caused by applying the summation convention to a pair of dummy indices that are bound to each other in an expression...

In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total. Beside numbers, other...

convenience, the Ricci calculus incorporates Einstein notation, which implies summation over indices repeated within a term and universal quantification over...

A_{1}B_{2}-B_{1}A_{2}]} , and can also be written in components, using Einstein summation convention as ( A × B ) i = ε i j k A j B k {\displaystyle (\mathbf {A} \times...

=dq^{i}dq^{j}\mathbf {h} _{i}\cdot \mathbf {h} _{j}} (with Einstein summation convention). The six independent scalar products gij=hi.hj of the natural basis...

Kronecker delta function is for filtering terms from an Einstein summation convention. The discrete unit sample function is more simply defined as: δ [...

inventors, such as Leibniz's notation, Legendre symbol, the Einstein summation convention, etc. General typesetting systems are generally not well suited for...

contraction between tensors by repeating indices as in the Einstein summation convention. Changing tetrads is a routine operation in the standard formalism...

{\partial u^{i}}{\partial x^{s}}}} where we have used the Einstein summation convention. Therefore, a tangent vector of a smooth curve will transform as...

Roger Penrose as a way to use the formal aspects of the Einstein summation convention to compensate for the difficulty in describing contractions and covariant...

may be determined using the following formula (using the Einstein summation convention), which is the component form of the pullback operation: g a b =...

infinite dimensional "functional manifold". In integrals, the Einstein summation convention is used. Alternatively, A i B i   = d e f   ∫ M ∑ α A α ( x ) B α...

{\displaystyle \partial \Omega } . Proof of Theorem. We use the Einstein summation convention. By using a partition of unity, we may assume that u {\displaystyle...

g^{ij}} is the inverse metric tensor, and the Einstein summation convention implies summation over i and j. If the coordinates are orthogonal we can easily...

Minkowski metric tensor of metric signature (− + + +) and the Einstein summation convention over repeated indices is used. Explicitly in matrix form: T μ ν =...

is a four-vector and is Lorentz covariant. This article uses the summation convention for indices. See covariance and contravariance of vectors for background...

{\displaystyle g} is the determinant of the metric tensor and the Einstein summation convention implies that repeated indices are summed over. Due to the symmetry...

see sign convention. The gravitation constant G {\displaystyle G} will be kept explicit. This article employs the Einstein summation convention, where repeated...