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...

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

(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...

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...

}^{cd\dots }} is the generalized Kronecker delta, and we use the Einstein notation to summation over like indices. More generally, irrespective of the...

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

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...

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