# Levi-Civita symbol

In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol represents a collection of numbers; defined from the sign of a permutation of the natural numbers 1, 2, ..., n, for some positive integer n. It is named after the Italian mathematician and physicist Tullio Levi-Civita. Other names include the permutation symbol, antisymmetric symbol, or alternating symbol, which refer to its antisymmetric property and definition in terms of permutations.
Ricci calculus
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern name for what used to be called the
In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to
Defining equation (physical chemistry)
In physical chemistry, there are numerous quantities associated with chemical compounds and reactions; notably in terms of amounts of substance, activity or concentration of a substance, and the rate of reaction. This article uses SI units
Defining equation (physics)
In physics, defining equations are equations that define new quantities in terms of base quantities. This article uses the current SI system of units, not natural or characteristic units
Antisymmetric tensor
In mathematics and theoretical physics, a tensor is antisymmetric on an index subset if it alternates sign (+/−) when any two indices of the subset are interchanged. The index subset must generally either be all covariant or all contravariant
Relativistic mechanics
In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving
Cartesian tensor
In geometry and linear algebra, a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from one such basis to another is through an orthogonal transformation
Outermorphism
In geometric algebra, the outermorphism of a linear function between vector spaces is a natural extension of the map to arbitrary multivectors. It is the unique unital algebra homomorphism of exterior algebras whose restriction to the vector spaces is the
Relativistic wave equations
In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. In the context of
Andrei Simonov
Andrei Dmitrievich Simonov was a Russian Armed Forces major general serving as Chief of the Electronic Warfare Troops of the 2nd Army of the Western Military District