In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with...

fundamental treatise on absolute differential calculus (also known as Ricci calculus) with coordinates or tensor calculus on Riemannian manifold, which then became...

2}\\a_{3}&b_{3}&c_{3}\end{vmatrix}}}.} Cramer's rule is used in the Ricci calculus in various calculations involving the Christoffel symbols of the first...

achieving brevity. As part of mathematics it is a notational subset of Ricci calculus; however, it is often used in physics applications that do not distinguish...

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian...

Voigt in 1898. Tensor calculus was developed around 1890 by Gregorio Ricci-Curbastro under the title absolute differential calculus, and originally presented...

propositional calculus, Ricci calculus, calculus of variations, lambda calculus, sequent calculus, and process calculus. Furthermore, the term "calculus" has variously...

equation Mathematics of general relativity Causal dynamical triangulation Ricci calculus Twisted geometries Tullio E. Regge (1961). "General relativity without...

For some history of the abstract theory see also multilinear algebra. Ricci calculus The earliest foundation of tensor theory – tensor index notation. Order...

In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various...

trace Interior product Raising and lowering indices Musical isomorphism Ricci calculus Let L(V, V) be the space of linear maps from V to V. Then the natural...

mathematics of general relativity Levi-Civita connection Parallel transport Ricci calculus Tensor derivative (continuum mechanics) List of formulas in Riemannian...

of vectors Einstein notation Ricci calculus Tensor (intrinsic definition) Two-point tensor D.C. Kay (1988). Tensor Calculus. Schaum’s Outlines, McGraw Hill...

i} and the theorem follows. Q.E.D. Einstein notation Index notation Ricci calculus Reed, M.; Simon, B. (1980). Methods of Modern Mathematical Physics:...

equation Mathematics of general relativity Numerical relativity Ricci calculus Einstein, Albert (1916). "The Foundation of the General Theory of Relativity"...

U V W X Y Z See also References Absolute differential calculus An older name of Ricci calculus Absolute geometry Also called neutral geometry, a synthetic...

a fiber bundlePages displaying wikidata descriptions as a fallback Ricci calculus – Tensor index notation for tensor-based calculations Spinor field –...

particular, are non-numerical. Thus it should not be confused with the Ricci calculus. The notation was introduced by Roger Penrose as a way to use the formal...

through the work of Gregorio Ricci-Curbastro and Tullio Levi-Civita, particularly in the form of absolute differential calculus within multilinear algebra...

indicated by delimiting the antisymmetrized indices by square brackets (see Ricci calculus): ( ∇ × A ) i j = ∇ i A j − ∇ j A i = 2 ∇ [ i A j ] {\displaystyle \left(\nabla...

concepts of the flow determined by a vector field Ricci calculus Vector Analysis, a textbook on vector calculus by Wilson, first published in 1901, which did...

electric and magnetic fields Maxwell stress tensor Poynting vector Ricci calculus Segre classification "All the stress–energy tensors explored above were...

diagram notation Matrix product state uses Penrose graphical notation Ricci calculus Spin networks Trace diagram Roger Penrose, "Applications of negative...

\rho \sigma }.} This formula is often called the Ricci identity. This is the classical method used by Ricci and Levi-Civita to obtain an expression for the...

spacetime Differentiable manifold List of formulas in Riemannian geometry Ricci calculus Riemann–Christoffel tensor Gauss–Codazzi equations Example computation...

notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation) Van der Waerden notation Voigt notation Tensor...

mathematics of general relativity Mathematics of general relativity Ricci calculus For the details, see Section 2.11, The Metric Tensor and the Classical...

of relativity Problems with Einstein's general theory of relativity Ricci calculus – Tensor index notation for tensor-based calculations Timeline of gravitational...

electromagnetism Electromagnetic stress–energy tensor Gluon field strength tensor Ricci calculus Riemann–Silberstein vector ^ By definition, T [ a b c ] = 1 3 ! ( T...

rather only how the shape of the body is distorted by the tidal force. The Ricci curvature, or trace component of the Riemann tensor contains precisely the...