differential geometry, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies...

with the Ricci calculus. The notation was introduced by Roger Penrose as a way to use the formal aspects of the Einstein summation convention to compensate...

(as opposed to those of covectors) are said to be contravariant. In Einstein notation (implicit summation over repeated index), contravariant components...

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

Summation notation may refer to: Capital-sigma notation, mathematical symbol for summation Einstein notation, summation over like-subscripted indices This...

forms Component-free treatment of tensors Cramer's rule Dual space Einstein notation Exterior algebra Inner product Outer product Kronecker delta Levi-Civita...

contrast, a dyad is specifically a dyadic tensor of rank one. Einstein notation This notation is based on the understanding that whenever a multidimensional...

vectors in three-dimensional Euclidean space, to be expressed in Einstein index notation. The Levi-Civita symbol is most often used in three and four dimensions...

set equal to each other and summed over. In Einstein notation this summation is built into the notation. The result is another tensor with order reduced...

constant G {\displaystyle G} will be kept explicit. This article employs the Einstein summation convention, where repeated indices are automatically summed over...

theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current...

physicist Albert Einstein's formula E = m c 2 {\displaystyle E=mc^{2}} is the quantitative representation in mathematical notation of mass–energy equivalence...

{\displaystyle \partial _{i}f} and f i {\displaystyle f_{i}}  : Written with Einstein notation, where repeated indices (i) are summed over. The gradient (or gradient...

in the article del in cylindrical and spherical coordinates. Using Einstein notation we can consider the divergence in general coordinates, which we write...

matrix A by producing another matrix, often denoted by AT (among other notations). The transpose of a matrix was introduced in 1858 by the British mathematician...

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

momentum. The Einstein tensor G {\displaystyle \mathbf {G} } is a tensor of order 2 defined over pseudo-Riemannian manifolds. In index-free notation it is defined...

In algebra, the Binet–Cauchy identity, named after Jacques Philippe Marie Binet and Augustin-Louis Cauchy, states that ( ∑ i = 1 n a i c i ) ( ∑ j = 1...

Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory...

Historical Museum (Einstein Museum) Einstein notation Frist Campus Center at Princeton University – room 302 is associated with Einstein. The center was...

also become smaller: 1 Kelvin per m becomes 0.001 Kelvin per mm. In Einstein notation, contravariant vectors and components of tensors are shown with superscripts...

\delta _{ab\dots }^{cd\dots }} is the generalized Kronecker delta, and the Einstein summation convention is in use. More generally, irrespective of the number...

. Note that the μ and ν summation indices range from 0 to 3: see Einstein notation. (Some authors alternatively use the negative metric signature of...

or no columns, called an empty matrix. The specifics of symbolic matrix notation vary widely, with some prevailing trends. Matrices are commonly written...

\{k\in \mathbb {N} :1\leq k\leq n\}} , and u i {\displaystyle u_{i}} is a notation for the image of i {\displaystyle i} by the function/vector u {\displaystyle...

contraction Tensor Processing Unit (TPU) Tensor rank decomposition Einstein Notation Spin network Orús, Román (5 August 2019). "Tensor networks for complex...

Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his general theory of relativity. Unlike the infinitesimal calculus...

) g μ ν {\displaystyle {^{(4)}}g_{\mu \nu }} . The text here uses Einstein notation in which summation over repeated indices is assumed. Two types of...

index of a ( 0 , 2 ) {\displaystyle (0,2)} tensor.) Ricci calculus Einstein notation Metric tensor Musical isomorphism Falling and rising factorials Dual...

In mathematics and physics, Penrose graphical notation or tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions...