differential geometry, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies...
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Glossary of tensor theory (redirect from Tensor notation)
contrast, a dyad is specifically a dyadic tensor of rank one. Einstein notation This notation is based on the understanding that whenever a multidimensional...
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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...
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Summation notation may refer to: Capital-sigma notation, mathematical symbol for summation Einstein notation, summation over like-subscripted indices This...
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Ricci calculus (redirect from Tensor index notation)
For compactness and convenience, the Ricci calculus incorporates Einstein notation, which implies summation over indices repeated within a term and universal...
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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...
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The Einstein tensor G {\displaystyle {\boldsymbol {G}}} is a tensor of order 2 defined over pseudo-Riemannian manifolds. In index-free notation it is...
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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...
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forms Component-free treatment of tensors Cramer's rule Dual space Einstein notation Exterior algebra Inner product Outer product Kronecker delta Levi-Civita...
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associated names for this idea: Mandel notation, Mandel–Voigt notation and Nye notation are others found. Kelvin notation is a revival by Helbig of old ideas...
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in the article del in cylindrical and spherical coordinates. Using Einstein notation we can consider the divergence in general coordinates, which we write...
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(as opposed to those of covectors) are said to be contravariant. In Einstein notation (implicit summation over repeated index), contravariant components...
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Binet–Cauchy identity (section Einstein notation)
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...
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physicist Albert Einstein's formula E = m c 2 {\displaystyle E=mc^{2}} is the quantitative representation in mathematical notation of mass–energy equivalence...
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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...
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which will also be mixed. Covariance and contravariance of vectors Einstein notation Ricci calculus Tensor (intrinsic definition) Two-point tensor D.C...
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Antisymmetric tensor (section Notation)
\delta _{ab\dots }^{cd\dots }} is the generalized Kronecker delta, and the Einstein summation convention is in use. More generally, irrespective of the number...
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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...
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Tensor (section Einstein summation convention)
the rightmost expression the summation sign was suppressed: this is the Einstein summation convention, which will be used throughout this article. The components...
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. 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...
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Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory...
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Historical Museum (Einstein Museum) Einstein notation Frist Campus Center at Princeton University – room 302 is associated with Einstein. The center was...
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constant G {\displaystyle G} will be kept explicit. This article employs the Einstein summation convention, where repeated indices are automatically summed over...
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\{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...
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Matrix (mathematics) (redirect from Matrix notation)
or no columns, called an empty matrix. The specifics of symbolic matrix notation vary widely, with some prevailing trends. Matrices are commonly written...
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Stress–energy tensor (section Einstein field equations)
superscripted variables (not exponents; see Tensor index notation and Einstein summation notation). If Cartesian coordinates in SI units are used, then the...
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In mathematics and physics, Penrose graphical notation or tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions...
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part of the curvature that exists in free space—a solution of the vacuum Einstein equation—and it governs the propagation of gravitational waves through...
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Christoffel symbols (category Mathematical notation)
and Einstein notation for summation) gjigik = δ jk. Although the Christoffel symbols are written in the same notation as tensors with index notation, they...
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