1,733 articles
Levi-Civita symbol
The Levi-Civita symbol, also called the permutation symbol, is a collection of numbers based on the sign of a permutation, equal to +1, −1, or 0.
Liber Abaci
Liber Abaci, also spelled Liber Abbaci, is a 1202 Latin treatise by Leonardo Pisano, known as Fibonacci, that taught calculation with Hindu-Arabic numerals and posed the rabbit problem behind the Fibonacci sequence.
Lie algebra
A Lie algebra is a vector space with a bilinear, antisymmetric Lie bracket satisfying the Jacobi identity, recording the infinitesimal behavior of continuous symmetry groups, named after Sophus Lie.
Lie algebra cohomology
Lie algebra cohomology, also called cohomology of Lie algebras, is a cohomology theory for Lie algebras introduced by Élie Cartan in 1929, computed via the Chevalley–Eilenberg complex.
Lie algebra extension
A Lie algebra extension is a Lie algebra fitting a short exact sequence, with splitting, central extensions, and classification by Lie algebra cohomology, founded by Chevalley and Eilenberg in 1948.
Lie algebra representation
A Lie algebra representation is a way of realizing a Lie algebra as linear operators on a vector space, via a bracket-preserving homomorphism into endomorphisms.
Lie bialgebra
A Lie bialgebra, or Poisson-Hopf algebra, is a Lie algebra with a compatible cobracket, introduced by Vladimir Drinfeld in 1983 as the structure underlying Poisson-Lie groups.
Lie group
A Lie group is a set carrying compatible structures of a group and a smooth manifold, named for Sophus Lie and central to continuous symmetry in mathematics and physics.
Lie superalgebra
A Lie superalgebra is a ℤ₂-graded algebra with even and odd parts whose bracket obeys graded symmetry and Jacobi identities, generalizing a Lie algebra and underlying supersymmetry in physics.
Limit (category theory)
In category theory, a limit of a diagram is a universal cone that every other cone factors through uniquely, generalizing products, equalizers, pullbacks, and terminal objects; it was named by Daniel Kan in 1958.
Limit ordinal
A limit ordinal is a nonzero ordinal number that has no immediate predecessor, so it is not the successor of any ordinal; the first example is ω, the smallest infinite ordinal.
Lindelöf hypothesis
The Lindelöf hypothesis, also known as the Lindelöf conjecture, is a 1908 conjecture of Ernst Leonard Lindelöf asserting the Riemann zeta function grows slowly on the critical line.
Lindemann–Weierstrass theorem
The Lindemann–Weierstrass theorem is a result in transcendental number theory, proved by Karl Weierstrass in 1885, stating that exponentials of distinct algebraic numbers are linearly independent over the algebraic numbers.
Lindenbaum–Tarski algebra
The Lindenbaum–Tarski algebra, also called the Lindenbaum algebra, is the algebra of formulas of a logic modulo provable equivalence, introduced by Lindenbaum and Tarski in 1926–27.
Line bundle
A line bundle is a vector bundle whose fiber at every point is one-dimensional; in algebraic geometry it appears as an invertible sheaf and encodes divisors.
Linear algebra
Linear algebra is the branch of mathematics that studies vector spaces and linear maps between them, together with the matrices, determinants, and eigenvalues used to compute with them.
Linear combination
A linear combination is an expression of the form c1v1 + ... + ckvk, formed by scaling vectors and adding them; it underlies span, independence, and bases.
Linear equation
A linear equation, also called a first-degree equation, is an algebraic equation where each variable appears only to the first power, as in ax + b = 0.
Linear function
A linear function, also called a linear map or linear transformation, is a function between vector spaces that preserves vector addition and scalar multiplication; it is represented by a matrix.
Linear independence
Linear independence is the property of a set of vectors where no vector is a linear combination of the others; it is half of the definition of a basis.
Linear map
A linear map, also called a linear transformation, is a function between vector spaces that preserves addition and scalar multiplication, exemplified by rotations and projections.
Linear span
The linear span, also called the linear hull, of a set of vectors is the set of all their finite linear combinations, and it forms the smallest subspace containing them.
Linear subspace
A linear subspace, also called a vector subspace, is a subset of a vector space that is itself a vector space under the same addition and scalar multiplication; examples include lines and planes through the origin.
Linear system of divisors
A linear system of divisors, also called a linear series, is a family of linearly equivalent effective divisors on an algebraic variety, parametrized by projective space.
Linearity
Linearity is the property of a function or system satisfying additivity and homogeneity, meaning T(u+v) = T(u)+T(v) and T(av) = aT(v); it enables superposition, unlike nonlinear problems.
Liouville function
The Liouville function is the completely multiplicative arithmetic function λ(n) = (−1)^Ω(n), counting prime factors with multiplicity; it is central to the prime number theorem and the Riemann hypothesis.
List of finite simple groups
The list of finite simple groups is the classification theorem's catalog: cyclic groups of prime order, alternating groups, groups of Lie type, and 26 sporadic groups.
List of finite-dimensional Nichols algebras
The list of finite-dimensional Nichols algebras collects the classified finite-dimensional examples, chiefly of diagonal type, with their generalized root systems, defining relations, and dimensions from Heckenberger's 2009 classification.
List of Indian mathematicians
The list of Indian mathematicians covers the documented figures of a tradition running from Vedic geometry through Aryabhata, Brahmagupta, the Kerala School's calculus, and the modern era of Ramanujan and the Tata Institute.
List of logarithmic identities
The list of logarithmic identities, also called the laws of logs, gives the product, quotient, power, and change-of-base rules used to expand and condense logarithms in algebra.