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  2. Einstein notation - Wikipedia

    en.wikipedia.org/wiki/Einstein_notation

    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.

  3. Help:Displaying a formula - Wikipedia

    en.wikipedia.org/wiki/Help:Displaying_a_formula

    When an inline formula is long enough, it can be helpful to allow it to break across lines. Whether using LaTeX or templates, split the formula at each acceptable breakpoint into separate <math> tags or {} templates with any binary relations or operators and intermediate whitespace included at the trailing rather than leading end of a part.

  4. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    2.1.8 Einstein tensor. 2.2 Identities. ... Printable version; In other projects ... Einstein notation is used throughout this article. This article uses the "analyst ...

  5. ADM formalism - Wikipedia

    en.wikipedia.org/wiki/ADM_formalism

    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.

  6. Classical electromagnetism and special relativity - Wikipedia

    en.wikipedia.org/wiki/Classical_electromagnetism...

    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 (+ − − −).

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  8. Introduction to the mathematics of general relativity - Wikipedia

    en.wikipedia.org/wiki/Introduction_to_the...

    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 ...

  9. Covariance and contravariance of vectors - Wikipedia

    en.wikipedia.org/wiki/Covariance_and_contra...

    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 ...