Every idea

Ideas 2101–2250 of 7806.

Name	Kind	Subject
Connected graph	Concept	Combinatorics
Reduction modulo p test for irreducibility	Theorem	Field theory and polynomials
Change of basis matrix	Definition	Linear and multilinear algebra; matrix theory
Radius of convergence of the binomial series	Proposition	Functions of a complex variable
Positive definite matrix	Concept	Linear and multilinear algebra; matrix theory
Usual metric on the real line	Example	General topology
Number of prime factors counted with multiplicity	Concept	Number theory
Splitting field	Concept	Field theory and polynomials
Continuous partial derivatives imply differentiability	Theorem	Real functions
Derivative of x^a	Theorem	Real functions
Stirling numbers of the first kind	Concept	Number theory
Discrete uniform distribution	Definition	Probability theory and stochastic processes
Quotient group	Concept	Group theory and generalizations
Lagrange's four-square theorem	Theorem	Number theory
Quadratic formula	Theorem	Field theory and polynomials
Trace of a linear map	Concept	Linear and multilinear algebra; matrix theory
Independent set	Definition	Combinatorics
Diffeomorphism	Concept	Global analysis, analysis on manifolds
Antisymmetric relation	Concept	Mathematical logic and foundations
Derivative of an inverse function	Theorem	Real functions
Block diagonal matrix	Definition	Linear and multilinear algebra; matrix theory
Linearity of differentiation	Theorem	Real functions
Intercept theorem	Theorem	Geometry
Convex function on R^n	Definition	Real functions
Bernoulli's inequality	Theorem	Real functions
Fermat's little theorem	Theorem	Number theory
Conjunction	Definition	Mathematical logic and foundations
Curl of a gradient is zero	Proposition	Real functions
Cayley's formula	Theorem	Combinatorics
The number of Sylow subgroups divides the index	Theorem	Group theory and generalizations
Analytic continuation	Concept	Functions of a complex variable
Four colour theorem	Theorem	Combinatorics
Binary operation	Concept	General algebraic systems
Uniform continuity	Concept	Real functions
Every linearly independent set extends to a basis	Theorem	Linear and multilinear algebra; matrix theory
Classification of the Platonic solids	Theorem	Geometry
Line integral of a scalar field	Definition	Real functions
Existence of inverses modulo n	Theorem	Number theory
The only ideals of a field are zero and the whole field	Proposition	Field theory and polynomials
Universal property of the product topology	Theorem	General topology
Elementary matrix	Definition	Linear and multilinear algebra; matrix theory
Pythagorean triple	Concept	Number theory
Euler's criterion	Theorem	Number theory
Complementary subspaces	Concept	Linear and multilinear algebra; matrix theory
Dual space	Definition	Linear and multilinear algebra; matrix theory
Equivalent norms	Concept	Functional analysis
Adjoining a root of a polynomial	Definition	Field theory and polynomials
Vieta's formulas	Theorem	Field theory and polynomials
Nilpotent endomorphism	Definition	Linear and multilinear algebra; matrix theory
Approximation property of the supremum	Proposition	Real functions
Coefficient of a power series	Definition	Commutative algebra
Incentre	Concept	Geometry
Step function	Definition	Real functions
Field generated by adjoining elements	Definition	Field theory and polynomials
Schwarz lemma	Lemma	Functions of a complex variable
Algebraic number	Definition	Number theory
Self-adjoint operator	Definition	Operator theory
Sum of ideals	Concept	Commutative algebra
Generators of a group	Concept	Group theory and generalizations
Monotonicity of the integral	Theorem	Real functions
A finite abelian group is cyclic iff its exponent equals its order	Proposition	Group theory and generalizations
Orthogonal projection is the closest point	Theorem	Functional analysis
Epsilon characterisation of Cauchy sequences	Proposition	General topology
Minimal element	Definition	Order, lattices, ordered algebraic structures
Algebraic closure	Definition	Field theory and polynomials
Complement graph	Concept	Combinatorics
Coprime ideals	Definition	Commutative algebra
Exterior algebra	Concept	Linear and multilinear algebra; matrix theory
Symmetric difference	Concept	Mathematical logic and foundations
Division algorithm for polynomials	Theorem	Commutative algebra
Norm induced by an inner product	Concept	Functional analysis
Derivative of a polynomial	Corollary	Real functions
Wronskian test for linear independence of solutions	Theorem	Ordinary differential equations
Every sequence has a monotone subsequence	Lemma	Sequences, series, summability
Matching	Concept	Combinatorics
Tree	Definition	Combinatorics
Upper triangular matrix	Definition	Linear and multilinear algebra; matrix theory
Change of basis matrix	Concept	Linear and multilinear algebra; matrix theory
Product of vector spaces	Definition	Linear and multilinear algebra; matrix theory
One-point compactification	Definition	General topology
A ring homomorphism is injective iff its kernel is zero	Proposition	Associative rings and algebras
Continuum hypothesis	Axiom	Mathematical logic and foundations
Derivative as a little-o approximation	Proposition	Real functions
Algebraic number	Concept	Number theory
Prime element	Definition	Commutative algebra
Geometric sequence	Definition	Sequences, series, summability
Product of rings	Definition	Associative rings and algebras
Line	Concept	Geometry
Diagonalisable iff the minimal polynomial has distinct roots	Theorem	Linear and multilinear algebra; matrix theory
Centre of mass	Definition	Real functions
Fundamental matrix	Definition	Ordinary differential equations
Compact Hausdorff spaces are normal	Theorem	General topology
Change of basis formula	Theorem	Linear and multilinear algebra; matrix theory
Normal matrix	Concept	Linear and multilinear algebra; matrix theory
Series of functions	Definition	Sequences, series, summability
A quotient is abelian iff the subgroup contains the commutator subgroup	Proposition	Group theory and generalizations
Test for exactness	Theorem	Ordinary differential equations
Existential quantifier	Concept	Mathematical logic and foundations
Order on the reals	Concept	Real functions
Alternating multilinear map	Definition	Linear and multilinear algebra; matrix theory
Contraction mapping	Definition	Operator theory
First isomorphism theorem for linear maps	Theorem	Linear and multilinear algebra; matrix theory
One-form	Definition	Global analysis, analysis on manifolds
Poisson point process	Concept	Probability theory and stochastic processes
e	Object	Number theory
Sequential continuity	Definition	Real functions
Noetherian ring	Definition	Commutative algebra
Exponentials dominate powers in sequences	Proposition	Real functions
Equicontinuity	Definition	General topology
Natural numbers	Object	Number theory
Divergence	Concept	Real functions
Hyperbolic tangent	Definition	Special functions
A series of nonnegative terms converges iff its partial sums are bounded	Proposition	Sequences, series, summability
Hausdorff space	Definition	General topology
Coupon collector's problem	Problem	Probability theory and stochastic processes
Mantel's theorem	Theorem	Combinatorics
Deficient number	Concept	Number theory
Perfect number	Concept	Number theory
Cumulative distribution function	Definition	Probability theory and stochastic processes
Open connected subsets of R^n are path-connected	Theorem	General topology
Marginal distribution	Concept	Statistics
Characteristic function	Definition	Probability theory and stochastic processes
Compact subsets of a Hausdorff space are closed	Proposition	General topology
Ideal	Definition	Commutative algebra
Power series	Concept	Functions of a complex variable
Separable extension	Definition	Field theory and polynomials
Subgroup	Definition	Group theory and generalizations
Well-ordering theorem	Theorem	Mathematical logic and foundations
Irrationality of square roots of non-squares	Theorem	Number theory
Riemann integrable function	Definition	Real functions
Matrix	Definition	Linear and multilinear algebra; matrix theory
Completeness via Cauchy sequences	Proposition	General topology
Radius of convergence	Concept	Functions of a complex variable
Symmetric matrix	Definition	Linear and multilinear algebra; matrix theory
A homomorphism is injective iff its kernel is trivial	Proposition	Group theory and generalizations
Cumulant generating function	Concept	Probability theory and stochastic processes
The rationals form a field	Theorem	Field theory and polynomials
Limits preserve non-strict inequalities	Proposition	Sequences, series, summability
Uniqueness quantifier	Definition	Mathematical logic and foundations
Composite number	Definition	Number theory
Liouville's theorem on Diophantine approximation	Theorem	Number theory
Hilbert's hotel	Example	Mathematical logic and foundations
Quotient map	Concept	Linear and multilinear algebra; matrix theory
Upper triangular matrix	Concept	Linear and multilinear algebra; matrix theory
Pairwise independence	Definition	Probability theory and stochastic processes
Boolean ring	Definition	Order, lattices, ordered algebraic structures
Square root of a positive semidefinite matrix	Definition	Linear and multilinear algebra; matrix theory
Falling factorial	Definition	Combinatorics
Cross product	Concept	Linear and multilinear algebra; matrix theory
Wronskian	Definition	Ordinary differential equations