Every idea

Ideas 301–450 of 7806.

Name	Kind	Subject
Topological property	Concept	General topology
Reduction of order	Concept	Ordinary differential equations
Polar form of a quadratic form	Definition	Linear and multilinear algebra; matrix theory
Cauchy mean value theorem	Theorem	Real functions
Closure is closed	Proposition	General topology
Decreasing sequence bounded below converges	Corollary	Sequences, series, summability
Greatest common divisor	Definition	Number theory
Riemann mapping theorem	Theorem	Functions of a complex variable
External direct sum	Definition	Linear and multilinear algebra; matrix theory
Bernoulli process	Definition	Probability theory and stochastic processes
Kernel of a linear map	Definition	Linear and multilinear algebra; matrix theory
Conditional convergence	Definition	Sequences, series, summability
Branch of the logarithm	Concept	Special functions
Centraliser	Concept	Group theory and generalizations
One-form	Concept	Global analysis, analysis on manifolds
Real and imaginary parts	Definition	Functions of a complex variable
K5 and K3,3 are not planar	Proposition	Combinatorics
Ideal generated by a subset	Definition	Commutative algebra
Partial fraction decomposition	Concept	Real functions
Commutative ring	Concept	Commutative algebra
Total order	Definition	Order, lattices, ordered algebraic structures
The real part of a holomorphic function is harmonic	Proposition	Potential theory
A tangent is perpendicular to the radius	Theorem	Geometry
Order of a cyclic subgroup equals the order of its generator	Proposition	Group theory and generalizations
Event	Concept	Probability theory and stochastic processes
Polyhedron	Concept	Convex and discrete geometry
Residue theorem	Theorem	Functions of a complex variable
Matrix multiplication	Concept	Linear and multilinear algebra; matrix theory
Order on the reals	Definition	Real functions
Projection	Concept	Linear and multilinear algebra; matrix theory
Nine-point circle	Concept	Geometry
Factorial formula for binomial coefficients	Theorem	Combinatorics
Limit inferior	Concept	Sequences, series, summability
Markov chain	Definition	Probability theory and stochastic processes
Formal power series	Concept	Commutative algebra
Formula for the modulus	Proposition	Functions of a complex variable
Tangent plane to a graph	Concept	Real functions
Triangularisation	Theorem	Linear and multilinear algebra; matrix theory
Hyperbolic cosine	Concept	Special functions
Statistic	Definition	Statistics
Gauss's lemma on quadratic residues	Lemma	Number theory
Dirichlet convolution	Concept	Number theory
Leibniz formula for pi	Theorem	Sequences, series, summability
System of linear differential equations	Concept	Ordinary differential equations
Arzelà–Ascoli theorem	Theorem	General topology
Bernoulli distribution	Concept	Probability theory and stochastic processes
Chromatic polynomial	Definition	Combinatorics
Freshman's dream	Theorem	Commutative algebra
Parametric equation of a line	Concept	Geometry
Characteristic polynomial	Definition	Linear and multilinear algebra; matrix theory
Integral of exp(-x) over the half line	Example	Sequences, series, summability
Independence of two events	Concept	Probability theory and stochastic processes
Taylor's theorem with the Peano remainder	Corollary	Approximations and expansions
Column space	Concept	Linear and multilinear algebra; matrix theory
Norm on the Gaussian integers	Definition	Number theory
Absorbing Markov chain	Concept	Probability theory and stochastic processes
Generalized Euclid's lemma	Proposition	Number theory
Modulo operation	Concept	Number theory
Law of total variance	Theorem	Probability theory and stochastic processes
Multivalued function	Concept	Real functions
Left coset	Concept	Group theory and generalizations
Variance of the normal distribution	Proposition	Probability theory and stochastic processes
Determinant of a linear map	Definition	Linear and multilinear algebra; matrix theory
Cauchy–Euler equation	Concept	Ordinary differential equations
Range of a function	Concept	Mathematical logic and foundations
Irreducible polynomial	Concept	Field theory and polynomials
Vector triple product	Proposition	Linear and multilinear algebra; matrix theory
Chain rule for Jacobian matrices	Corollary	Real functions
Absolutely convergent improper integral	Definition	Sequences, series, summability
Dimension	Concept	Linear and multilinear algebra; matrix theory
Pythagorean trigonometric identity	Theorem	Special functions
P-adic valuation	Concept	Number theory
Antichain	Concept	Order, lattices, ordered algebraic structures
Triangle inequality	Theorem	Real functions
Mean value theorem in several variables	Theorem	Real functions
Regular space	Concept	General topology
Perpendicular bisector	Definition	Geometry
Normed vector space	Concept	Functional analysis
Separable polynomial	Definition	Field theory and polynomials
Wilson's theorem	Theorem	Number theory
Equivalence of norms in finite dimension	Theorem	Functional analysis
de Moivre's formula	Theorem	Special functions
Type I and type II errors	Concept	Statistics
Path	Concept	Combinatorics
Minimal polynomial	Concept	Linear and multilinear algebra; matrix theory
Vectors are perpendicular if and only if their dot product is zero	Proposition	Geometry
Torus	Example	Manifolds and cell complexes
Cauchy–Schwarz inequality for expectations	Theorem	Probability theory and stochastic processes
Second-countable space	Concept	General topology
A matrix is invertible iff its determinant is a unit	Theorem	Linear and multilinear algebra; matrix theory
Complement principle	Proposition	Combinatorics
Taylor's theorem	Theorem	Approximations and expansions
Skew-symmetric matrix	Definition	Linear and multilinear algebra; matrix theory
Formula for the number of derangements	Theorem	Combinatorics
Limit of a quotient of sequences	Proposition	Sequences, series, summability
Continuous linear map	Concept	Operator theory
Integers modulo n	Concept	Number theory
Indefinite integral	Definition	Real functions
Circumcircle	Concept	Geometry
Jacobian determinant	Definition	Real functions
Complete graph	Example	Combinatorics
Number of derangements	Definition	Combinatorics
Sum of a finite geometric progression	Theorem	Combinatorics
Multiplicity of a root	Definition	Commutative algebra
Sample mean	Concept	Statistics
Open mapping theorem	Theorem	Functions of a complex variable
Oriented angle	Concept	Geometry
The Dirichlet function is not Riemann integrable	Counterexample	Real functions
C^1 vector fields satisfy the Picard–Lindelöf hypotheses	Proposition	Ordinary differential equations
Binet's formula	Theorem	Number theory
Integer partition	Definition	Combinatorics
Lebesgue number lemma	Lemma	General topology
Lattice path	Concept	Combinatorics
Entire function	Definition	Functions of a complex variable
Nilpotent matrix	Definition	Linear and multilinear algebra; matrix theory
Direct sum of subspaces	Definition	Linear and multilinear algebra; matrix theory
Subgroups of a finite cyclic group correspond to divisors of its order	Theorem	Group theory and generalizations
Rational canonical form	Theorem	Linear and multilinear algebra; matrix theory
Continuous bijection from a compact space to a Hausdorff space is a homeomorphism	Theorem	General topology
Uniform limits of holomorphic functions are holomorphic	Theorem	Functions of a complex variable
Fermat's theorem on sums of two squares	Theorem	Number theory
Maclaurin series	Definition	Approximations and expansions
Multilinear map	Concept	Linear and multilinear algebra; matrix theory
Product metric	Definition	General topology
Diagonal matrix	Concept	Linear and multilinear algebra; matrix theory
Random variable with a density	Concept	Probability theory and stochastic processes
Circle	Definition	Geometry
The derangement numbers count derangements	Theorem	Combinatorics
Disc of convergence	Definition	Functions of a complex variable
Closed curve	Concept	Differential geometry
Monotonicity of probability	Proposition	Probability theory and stochastic processes
Homogeneous linear system with constant coefficients	Concept	Ordinary differential equations
Evaluation of real integrals by residues	Concept	Functions of a complex variable
Variance	Concept	Probability theory and stochastic processes
Every real number has a decimal expansion	Theorem	Number theory
Jacobian matrix	Concept	Real functions
Parseval's identity	Theorem	Functional analysis
Multiplicity of a root	Concept	Commutative algebra
Maximum modulus principle	Theorem	Functions of a complex variable
Concyclic points	Concept	Geometry
Open cover	Concept	General topology
Lagrange multiplier with one constraint	Corollary	Operations research, mathematical programming
Greedy colouring	Concept	Combinatorics
Möbius strip	Example	Manifolds and cell complexes
Exponential of a sum of commuting matrices	Theorem	Linear and multilinear algebra; matrix theory
Complementary subspaces	Definition	Linear and multilinear algebra; matrix theory
Field	Concept	Field theory and polynomials
log x is at most x - 1	Proposition	Special functions
Real sequence	Concept	Sequences, series, summability
Local maximum and minimum	Definition	Real functions