Nodes at W0, stub

A tag, a kind, a name, an inventory row, and a same_as or a source.

Ideas 1051–1200 of 6044.

Name	Kind	Subject
Monotone sequence	Definition	Sequences, series, summability
Ring isomorphism	Concept	Associative rings and algebras
The exponential function is strictly increasing	Proposition	Special functions
Restriction of an endomorphism to an invariant subspace	Concept	Linear and multilinear algebra; matrix theory
Maximum degree	Definition	Combinatorics
p-norm on R^n	Example	Functional analysis
Homogeneous linear equation	Concept	Ordinary differential equations
Stationary distribution	Concept	Probability theory and stochastic processes
Continuity at a point	Concept	General topology
Symmetric bilinear form associated with a quadratic form	Concept	Linear and multilinear algebra; matrix theory
Equivalence relation induced by a function	Concept	Mathematical logic and foundations
Variance under scaling	Proposition	Probability theory and stochastic processes
Diameter of a set	Concept	General topology
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
Number of prime factors counted with multiplicity	Concept	Number theory
Continuous partial derivatives imply differentiability	Theorem	Real functions
Derivative of x^a	Theorem	Real functions
Trace of a linear map	Concept	Linear and multilinear algebra; matrix theory
Linearity of differentiation	Theorem	Real functions
Convex function on R^n	Definition	Real functions
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
Every linearly independent set extends to a basis	Theorem	Linear and multilinear algebra; matrix theory
Classification of the Platonic solids	Theorem	Geometry
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
Adjoining a root of a polynomial	Definition	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
Field generated by adjoining elements	Definition	Field theory and polynomials
Sum of ideals	Concept	Commutative algebra
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
Coprime ideals	Definition	Commutative algebra
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
Change of basis matrix	Concept	Linear and multilinear algebra; matrix theory
A ring homomorphism is injective iff its kernel is zero	Proposition	Associative rings and algebras
Derivative as a little-o approximation	Proposition	Real functions
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
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
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
Sequential continuity	Definition	Real functions
Exponentials dominate powers in sequences	Proposition	Real functions
A series of nonnegative terms converges iff its partial sums are bounded	Proposition	Sequences, series, summability
Coupon collector's problem	Problem	Probability theory and stochastic processes
Mantel's theorem	Theorem	Combinatorics
Open connected subsets of R^n are path-connected	Theorem	General topology
Marginal distribution	Concept	Statistics
Compact subsets of a Hausdorff space are closed	Proposition	General topology
Irrationality of square roots of non-squares	Theorem	Number theory
Riemann integrable function	Definition	Real functions
Completeness via Cauchy sequences	Proposition	General topology
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
Liouville's theorem on Diophantine approximation	Theorem	Number theory
Quotient map	Concept	Linear and multilinear algebra; matrix theory
Pairwise independence	Definition	Probability theory and stochastic processes
Square root of a positive semidefinite matrix	Definition	Linear and multilinear algebra; matrix theory
Idempotent element	Concept	Associative rings and algebras
Classification of conics by the discriminant	Theorem	Geometry
Degree of a simple extension is the degree of the minimal polynomial	Corollary	Field theory and polynomials
Fermat primality test	Concept	Number theory
Eigenvector	Concept	Linear and multilinear algebra; matrix theory
Classification of equilibria of planar linear systems	Concept	Ordinary differential equations
Equilibrium point	Concept	Ordinary differential equations
Mean value theorem for integrals	Theorem	Real functions
Discrete metric	Example	General topology
exp(1/z) has an essential singularity at 0	Example	Functions of a complex variable
Asymptotic stability	Concept	Ordinary differential equations
The integral of a continuous function is an antiderivative	Corollary	Real functions
Right coset	Concept	Group theory and generalizations
Implicit function theorem for a surjective derivative	Corollary	Real functions
Double negation law	Theorem	Mathematical logic and foundations
The minimal polynomial is irreducible	Proposition	Field theory and polynomials
Variance as the mean of the square minus the square of the mean	Proposition	Probability theory and stochastic processes
Epsilon-net characterisation of total boundedness	Proposition	General topology
Transvection	Definition	Linear and multilinear algebra; matrix theory
Birthday problem	Example	Probability theory and stochastic processes
Trace is the sum of the eigenvalues	Theorem	Linear and multilinear algebra; matrix theory
Closed formula for Catalan numbers	Theorem	Combinatorics
Schwarz's theorem for C^2 functions	Theorem	Real functions
Reduced row echelon form	Definition	Linear and multilinear algebra; matrix theory
Triangle inequality for integrals	Theorem	Real functions
Composition of continuous functions is continuous	Proposition	Real functions
Connected components are closed	Proposition	General topology
Characteristic function of the normal distribution	Proposition	Probability theory and stochastic processes
Derivative of a map into R^n by components	Proposition	Real functions
Product of two subgroups	Definition	Group theory and generalizations
Construction of the integers from the natural numbers	Concept	Number theory
Discrete Grönwall inequality	Lemma	Real functions
Z/pZ is a field for p prime	Theorem	Number theory
Multiplicativity of the Legendre symbol	Theorem	Number theory
Second Borel–Cantelli lemma	Lemma	Probability theory and stochastic processes
Euclidean isometry	Definition	Geometry
Adjoining a root of a polynomial	Concept	Field theory and polynomials
Closed map	Definition	General topology
Angle-angle similarity	Theorem	Geometry
Classification of isometries of the plane	Theorem	Geometry
Subgraph	Definition	Combinatorics
Matrix of a bilinear form	Definition	Linear and multilinear algebra; matrix theory
Second-order Taylor expansion	Corollary	Real functions
Negation of a universal statement	Theorem	Mathematical logic and foundations
Glide reflection	Definition	Geometry
Sine is 2π-periodic	Theorem	Special functions
Non-commutativity of matrix multiplication	Counterexample	Linear and multilinear algebra; matrix theory
A function with bounded derivative is Lipschitz	Corollary	Real functions
Compactness via open covers	Proposition	General topology
Coefficient matrix	Definition	Linear and multilinear algebra; matrix theory
Composition of an integer	Concept	Combinatorics
Faithful action	Concept	Group theory and generalizations
Linearity of expectation	Theorem	Probability theory and stochastic processes
Vandermonde determinant	Theorem	Linear and multilinear algebra; matrix theory
Limit superior	Definition	Sequences, series, summability
Action by conjugation	Example	Group theory and generalizations
The exponential function is positive	Proposition	Special functions
Metric spaces are Hausdorff	Proposition	General topology
Existence of a complementary subspace	Theorem	Linear and multilinear algebra; matrix theory
Continuity is equivalent to sequential continuity	Theorem	Real functions
Jordan block	Definition	Linear and multilinear algebra; matrix theory
Annihilating polynomial	Concept	Linear and multilinear algebra; matrix theory
Order of the symmetric group	Proposition	Group theory and generalizations
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
Restriction of an endomorphism to an invariant subspace	Definition	Linear and multilinear algebra; matrix theory
First supplement to quadratic reciprocity	Theorem	Number theory