6,052 articles
Symmetric cone
A symmetric cone is a closed convex cone that is homogeneous and self-dual, corresponding one-to-one to Euclidean Jordan algebras and serving as the setting for symmetric-cone optimization.
Symmetric design
A symmetric design is a balanced incomplete block design with equally many blocks and points, so every block contains k points and every pair of points lies in λ blocks.
Symmetric difference
The symmetric difference, also called the disjunctive union, is the set operation containing elements that belong to exactly one of two sets, corresponding to XOR in logic.
Symmetric function
A symmetric function is a function of several variables whose value does not change under any permutation of its variables; most often it means a symmetric polynomial in n variables.
Symmetric group
The symmetric group on a set is the group of all permutations of the set under composition; on n elements it is written Sn and has n! elements.
Symmetric matrix
A symmetric matrix is a square matrix that equals its own transpose, with entry i, j equal to entry j, i; all its eigenvalues are real.
Symmetric power
The symmetric power Sym^n(V), or n-fold symmetric power, turns a module V into degree-n homogeneous polynomial expressions in its elements, a quotient of the tensor power that forgets factor order.
Symmetric space
A symmetric space is a Riemannian manifold in which the geodesic symmetry at every point is induced by an isometry, a class introduced and classified by Élie Cartan.
Symmetric tensor
A symmetric tensor is a multidimensional array, the higher-order generalization of a symmetric matrix, whose entries are unchanged by any permutation of their indices, with uses in signal processing and machine learning.
Symmetry
Symmetry is the invariance of an object under a transformation: a snowflake rotated 60° about its center looks exactly as before, a key idea in mathematics and physics.
Symmetry group
A symmetry group is the group of all transformations, including rotations, reflections, and translations, that leave a figure, molecule, or crystal pattern unchanged, mapping it onto itself.
Symplectic field theory
Symplectic field theory, introduced by Yakov Eliashberg, Alexander Givental, and Helmut Hofer in 2000, counts punctured pseudoholomorphic curves to produce algebraic invariants of contact manifolds and their Legendrian submanifolds.
Symplectic form
A symplectic form is a closed, nondegenerate differential 2-form on a smooth manifold, necessarily even-dimensional, that underlies symplectic geometry and provides the mathematical framework for Hamiltonian mechanics.
Symplectic group
The symplectic group is the classical group of matrices A satisfying AᵗJA = J, named by Hermann Weyl in 1939 and central to symplectic geometry and Hamiltonian mechanics.
Symplectic Lie algebra
The symplectic Lie algebra sp(2n, k) is the Lie algebra of endomorphisms of a 2n-dimensional space preserving a symplectic form, with dimension n(2n+1) and applications in Hamiltonian mechanics.
Symplectic manifold
A symplectic manifold is an even-dimensional differentiable manifold equipped with a closed, nondegenerate 2-form called a symplectic form, and it is the natural geometric setting for Hamiltonian mechanics.
Symplectic reduction
Symplectic reduction is a construction in symplectic geometry and Hamiltonian mechanics that quotients a symplectic manifold by a symmetry group, producing a lower-dimensional reduced space.
SymPy
SymPy is a free, open-source Python library for symbolic mathematics, written entirely in Python and started by Ondřej Čertík in 2006, covering calculus, algebra, and equation solving.
Synchronization of chaos
Synchronization of chaos is the process by which coupled or commonly driven chaotic systems converge to a common behavior, established by Pecora and Carroll's 1990 drive-response scheme.
Synthetic control method
The synthetic control method (SCM), proposed by Alberto Abadie and Javier Gardeazabal in 2003, estimates an intervention's effect by using a weighted combination of untreated units as the counterfactual.
Synthetic data
Synthetic data are artificial records generated from models fitted to confidential data, released so analysts can work without seeing real respondent values, a method proposed by Donald B. Rubin in 1993.
Synthetic difference-in-differences
Synthetic difference-in-differences (SDID) is an estimator for causal effects with panel data that combines synthetic control weighting with difference-in-differences regression, introduced by Athey, Imbens, Wager, and coauthors.
Systat
Systat is a statistics and statistical graphics software package for personal computers, created by Leland Wilkinson in the late 1970s and sold to SPSS in 1995.
System F
System F, also called the polymorphic lambda calculus or second-order lambda calculus, is a typed lambda calculus in which terms abstract over types, introduced by Jean-Yves Girard around 1970 and John C. Reynolds in 1974.
System L (logic)
System L is a name used in formal logic for several distinct deductive systems, chiefly Łukasiewicz's Hilbert-style axiomatization of classical propositional logic and the Curien–Herbelin term syntax for classical sequent calculus.
System of linear equations
A system of linear equations, also called simultaneous linear equations, is a collection of linear equations in unknown variables, solved by direct or iterative methods.
System T
System T, also called Gödel's T, is a quantifier-free theory of functionals of finite type introduced by Kurt Gödel in 1958 as the target of his Dialectica interpretation.
Systematic review
A systematic review, also called a systematic literature review, is a research synthesis answering a pre-specified question, with study eligibility criteria fixed in advance, unlike a narrative review.
Systematic sampling
Systematic sampling is a probability sampling design in which units are selected at a fixed interval through an ordered list after one random starting point.
Szemerédi regularity lemma
The Szemerédi regularity lemma, or Szemerédi's lemma, is a graph theory theorem stating every large dense graph can be partitioned so that most class pairs behave randomly, introduced by Endre Szemerédi.