Every idea

Ideas 2401–2550 of 7806.

Name	Kind	Subject
Annihilating polynomial	Concept	Linear and multilinear algebra; matrix theory
Monty Hall problem	Problem	Probability theory and stochastic processes
Skew-symmetric matrix	Concept	Linear and multilinear algebra; matrix theory
Order of the symmetric group	Proposition	Group theory and generalizations
Multinomial coefficient	Concept	Combinatorics
Fermat's theorem on stationary points	Theorem	Real functions
Circuit	Definition	Combinatorics
Converse of Lagrange's theorem fails for the alternating group A4	Counterexample	Group theory and generalizations
Matrix–vector product	Concept	Linear and multilinear algebra; matrix theory
Transitive closure	Definition	Mathematical logic and foundations
Algebraically closed field	Concept	Field theory and polynomials
Restriction of an endomorphism to an invariant subspace	Definition	Linear and multilinear algebra; matrix theory
Divisibility	Concept	Number theory
Moment	Definition	Probability theory and stochastic processes
Generating function	Concept	Combinatorics
First supplement to quadratic reciprocity	Theorem	Number theory
Bernoulli trial	Concept	Probability theory and stochastic processes
Null space	Concept	Linear and multilinear algebra; matrix theory
Residue	Concept	Functions of a complex variable
Heine–Borel theorem in finite-dimensional normed spaces	Theorem	Functional analysis
Composition factors	Concept	Group theory and generalizations
Multi-index notation	Concept	Real functions
Alternating series test	Theorem	Sequences, series, summability
Conservative vector field	Concept	Real functions
Limit of a function	Concept	Real functions
Projections are continuous	Proposition	General topology
Klein four-group	Object	Group theory and generalizations
Order of an inverse	Proposition	Group theory and generalizations
The continued fraction of a rational number terminates	Theorem	Number theory
The Gaussian integers are a Euclidean domain	Theorem	Number theory
Argument principle	Theorem	Functions of a complex variable
Farey sequence	Definition	Number theory
The constructible numbers form a field closed under square roots	Theorem	Field theory and polynomials
Jordan's lemma	Lemma	Functions of a complex variable
Random variable	Concept	Probability theory and stochastic processes
Interior is open	Proposition	General topology
Beta distribution	Definition	Probability theory and stochastic processes
Determinant is multilinear in the rows	Proposition	Linear and multilinear algebra; matrix theory
Second isomorphism theorem	Theorem	Group theory and generalizations
Null space	Definition	Linear and multilinear algebra; matrix theory
Probability of the complement	Proposition	Probability theory and stochastic processes
Alternating sum of binomial coefficients	Theorem	Combinatorics
Principal axis theorem	Theorem	Linear and multilinear algebra; matrix theory
Dirichlet convolution of multiplicative functions is multiplicative	Theorem	Number theory
Angle between two vectors	Definition	Geometry
Identity function	Concept	Mathematical logic and foundations
Moore–Penrose inverse	Definition	Linear and multilinear algebra; matrix theory
Product of two subgroups	Concept	Group theory and generalizations
Algebraic extension	Concept	Field theory and polynomials
Endomorphism	Definition	Linear and multilinear algebra; matrix theory
Linear congruence	Concept	Number theory
Maximal ideal	Concept	Commutative algebra
Expectation with respect to the binomial distribution	Proposition	Probability theory and stochastic processes
Injective function	Definition	Mathematical logic and foundations
The exponential series has infinite radius of convergence	Proposition	Functions of a complex variable
Infinite set	Concept	Mathematical logic and foundations
Cauchy sequence	Concept	Sequences, series, summability
Orthogonal complement of the orthogonal complement	Proposition	Functional analysis
Commutator of two elements	Concept	Group theory and generalizations
Liouville number	Concept	Number theory
Composition of relations	Concept	Mathematical logic and foundations
Affine subspace	Concept	Geometry
Closed ball	Concept	General topology
Centraliser	Definition	Group theory and generalizations
Interval	Concept	Real functions
Exact equation	Concept	Ordinary differential equations
Singular solution	Concept	Ordinary differential equations
Internal direct product	Definition	Group theory and generalizations
Cumulant generating function	Definition	Probability theory and stochastic processes
Stolz–Cesàro theorem	Theorem	Sequences, series, summability
Image of a set	Definition	Mathematical logic and foundations
Integral of a power	Proposition	Real functions
Linear equation	Concept	Linear and multilinear algebra; matrix theory
Domain	Concept	Mathematical logic and foundations
Arc length parametrisation	Concept	Differential geometry
Uniform continuity	Definition	Real functions
Second derivative	Concept	Real functions
Darboux's theorem	Theorem	Real functions
Statistic	Concept	Statistics
Derived series	Concept	Group theory and generalizations
Galois group of a polynomial	Concept	Field theory and polynomials
Permutation matrix	Definition	Linear and multilinear algebra; matrix theory
Regular graph	Concept	Combinatorics
The sequence r^n tends to zero for \|r\| < 1	Example	Sequences, series, summability
Holomorphic functions with nonzero derivative are conformal	Proposition	Functions of a complex variable
Nilpotent group	Concept	Group theory and generalizations
Conjugacy class	Definition	Group theory and generalizations
Orientation of a real vector space	Definition	Linear and multilinear algebra; matrix theory
Third Sylow theorem	Theorem	Group theory and generalizations
Orthogonal projection	Definition	Linear and multilinear algebra; matrix theory
Outer automorphism group	Concept	Group theory and generalizations
Polynomial ring	Definition	Commutative algebra
Diagonal matrix	Definition	Linear and multilinear algebra; matrix theory
Convergence in probability	Concept	Probability theory and stochastic processes
Field	Definition	Field theory and polynomials
Uniqueness quantifier	Concept	Mathematical logic and foundations
Joint probability distribution	Definition	Statistics
Probability distribution	Definition	Probability theory and stochastic processes
Subspace metric	Concept	General topology
Reciprocal rule	Proposition	Real functions
Contour line	Concept	Real functions
Characteristic equation	Definition	Ordinary differential equations
Equivalence relation induced by a function	Definition	Mathematical logic and foundations
Sequence	Definition	Sequences, series, summability
Closure	Concept	General topology
Holomorphic functions are infinitely differentiable	Corollary	Functions of a complex variable
Alternating series	Concept	Sequences, series, summability
Cayley–Hamilton theorem for linear maps	Theorem	Linear and multilinear algebra; matrix theory
Infimum	Concept	Order, lattices, ordered algebraic structures
Eigenvalues are the roots of the minimal polynomial	Theorem	Linear and multilinear algebra; matrix theory
Peano axioms	Concept	Mathematical logic and foundations
The algebraic numbers form a field	Theorem	Number theory
Gauss's lemma	Theorem	Commutative algebra
Fundamental solution of Pell's equation	Concept	Number theory
Removable discontinuity	Definition	Real functions
Stochastic process	Concept	Probability theory and stochastic processes
Predicate	Concept	Mathematical logic and foundations
Differential form	Definition	Global analysis, analysis on manifolds
Affine map	Definition	Geometry
Irrationality of pi	Theorem	Number theory
Orientation of a real vector space	Concept	Linear and multilinear algebra; matrix theory
Matrix of a bilinear form	Concept	Linear and multilinear algebra; matrix theory
Dimension of the coordinate space	Proposition	Linear and multilinear algebra; matrix theory
Implicit differentiation	Concept	Real functions
Derivative function	Concept	Real functions
Cardinal number	Definition	Mathematical logic and foundations
Euclidean domains are principal ideal domains	Theorem	Commutative algebra
Element	Concept	Mathematical logic and foundations
Product of rings	Concept	Associative rings and algebras
Riemann integral	Definition	Real functions
The Galois group has order at most the degree	Theorem	Field theory and polynomials
Orthocentre	Definition	Geometry
Galois extension	Concept	Field theory and polynomials
Euclidean vector	Concept	Geometry
Contraction mapping	Concept	Operator theory
Constructible number	Concept	Field theory and polynomials
Sample mean	Definition	Statistics
Lipschitz continuity	Definition	Real functions
Ratio test	Theorem	Sequences, series, summability
Transitive action	Definition	Group theory and generalizations
Compact space	Definition	General topology
Von Dyck's theorem	Theorem	Group theory and generalizations
Cycle graph	Example	Combinatorics
Positive definite matrix	Definition	Linear and multilinear algebra; matrix theory
Derivative of a map into a product	Proposition	Real functions
Number of odd-degree vertices is even	Corollary	Combinatorics
Linear differential equation of order n	Concept	Ordinary differential equations
Asymptotic equivalence	Concept	Approximations and expansions
Orthogonal matrix	Definition	Linear and multilinear algebra; matrix theory
In a UFD irreducible elements are prime	Theorem	Commutative algebra