Nodes at W0, stub

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

Ideas 151–300 of 6044.

Name	Kind	Subject
Polynomial evaluation	Concept	Commutative algebra
Intermediate field	Definition	Field theory and polynomials
The complex exponential is 2πi-periodic	Proposition	Special functions
Sum of the roots of unity	Proposition	Number theory
Complex logarithm	Concept	Special functions
Higher partial derivatives	Definition	Real functions
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
External direct sum	Definition	Linear and multilinear algebra; matrix theory
Bernoulli process	Definition	Probability theory and stochastic processes
Branch of the logarithm	Concept	Special functions
Centraliser	Concept	Group theory and generalizations
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
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
Order on the reals	Definition	Real functions
Factorial formula for binomial coefficients	Theorem	Combinatorics
Limit inferior	Concept	Sequences, series, summability
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
Gauss's lemma on quadratic residues	Lemma	Number theory
System of linear differential equations	Concept	Ordinary differential equations
Parametric equation of a line	Concept	Geometry
Integral of exp(-x) over the half line	Example	Sequences, series, summability
Taylor's theorem with the Peano remainder	Corollary	Approximations and expansions
Norm on the Gaussian integers	Definition	Number theory
Absorbing Markov chain	Concept	Probability theory and stochastic processes
Generalized Euclid's lemma	Proposition	Number theory
Law of total variance	Theorem	Probability theory and stochastic processes
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
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
Mean value theorem in several variables	Theorem	Real functions
Perpendicular bisector	Definition	Geometry
Type I and type II errors	Concept	Statistics
Vectors are perpendicular if and only if their dot product is zero	Proposition	Geometry
Cauchy–Schwarz inequality for expectations	Theorem	Probability theory and stochastic processes
A matrix is invertible iff its determinant is a unit	Theorem	Linear and multilinear algebra; matrix theory
Complement principle	Proposition	Combinatorics
Formula for the number of derangements	Theorem	Combinatorics
Limit of a quotient of sequences	Proposition	Sequences, series, summability
Integers modulo n	Concept	Number theory
Jacobian determinant	Definition	Real functions
Number of derangements	Definition	Combinatorics
Sum of a finite geometric progression	Theorem	Combinatorics
Multiplicity of a root	Definition	Commutative algebra
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
Lebesgue number lemma	Lemma	General topology
Lattice path	Concept	Combinatorics
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
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
Product metric	Definition	General topology
Random variable with a density	Concept	Probability theory and stochastic processes
The derangement numbers count derangements	Theorem	Combinatorics
Disc of convergence	Definition	Functions of a complex variable
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
Every real number has a decimal expansion	Theorem	Number theory
Multiplicity of a root	Concept	Commutative algebra
Lagrange multiplier with one constraint	Corollary	Operations research, mathematical programming
Greedy colouring	Concept	Combinatorics
Exponential of a sum of commuting matrices	Theorem	Linear and multilinear algebra; matrix theory
log x is at most x - 1	Proposition	Special functions
Real sequence	Concept	Sequences, series, summability
Local maximum and minimum	Definition	Real functions
Determinant is multiplicative	Theorem	Linear and multilinear algebra; matrix theory
Spectral theorem for normal matrices	Theorem	Linear and multilinear algebra; matrix theory
Variance under translation	Proposition	Probability theory and stochastic processes
Coordinate vector	Concept	Linear and multilinear algebra; matrix theory
Order of a group is the index times the order of the subgroup	Theorem	Group theory and generalizations
Modular exponentiation	Concept	Number theory
Uniqueness of the supremum	Proposition	Order, lattices, ordered algebraic structures
Mesh of a partition	Definition	Real functions
Divisibility in a commutative ring	Definition	Commutative algebra
Riesz representation theorem in finite dimensions	Theorem	Functional analysis
Density of the irrationals	Theorem	Real functions
Consistent and inconsistent systems	Definition	Linear and multilinear algebra; matrix theory
Dirichlet's approximation theorem	Theorem	Number theory
Infimum	Definition	Order, lattices, ordered algebraic structures
Homogeneous system of linear equations	Concept	Linear and multilinear algebra; matrix theory
Almost sure convergence	Definition	Probability theory and stochastic processes
Cyclic groups are abelian	Proposition	Group theory and generalizations
Law of total expectation	Theorem	Probability theory and stochastic processes
Galois field	Object	Field theory and polynomials
Chinese remainder theorem for non-coprime moduli	Theorem	Number theory
Solution of an ordinary differential equation	Definition	Ordinary differential equations
Contrapositive	Theorem	Mathematical logic and foundations
Higher derivative	Concept	Real functions
Little o notation	Definition	Approximations and expansions
Continued fraction expansion of a real number	Concept	Number theory
Multiplicativity of the divisor function	Theorem	Number theory
Integral of cosine	Proposition	Real functions
Determinant as signed volume	Concept	Linear and multilinear algebra; matrix theory
Existence of primitive roots modulo a prime	Theorem	Number theory
Every connected graph has a spanning tree	Theorem	Combinatorics
Monotone functions are Riemann integrable	Theorem	Real functions
Cardinality of a finite set	Definition	Mathematical logic and foundations
Harmonic conjugate	Concept	Potential theory
The real numbers are uncountable	Theorem	Mathematical logic and foundations
Classical definition of probability	Concept	Probability theory and stochastic processes
Product of a matrix and its adjugate	Theorem	Linear and multilinear algebra; matrix theory
Annihilating polynomial	Definition	Linear and multilinear algebra; matrix theory
Associate elements	Definition	Commutative algebra
Eigenvalues are the roots of the characteristic polynomial	Theorem	Linear and multilinear algebra; matrix theory
Converse relation	Concept	Mathematical logic and foundations
Compact iff complete and totally bounded	Theorem	General topology
Fermat numbers are pairwise coprime	Theorem	Number theory
PID implies UFD	Theorem	Commutative algebra
Perpendicular bisector	Concept	Geometry
Sequential continuity	Concept	Real functions
Lebesgue's criterion for Riemann integrability	Theorem	Real functions
A matrix is diagonalisable iff it has a basis of eigenvectors	Theorem	Linear and multilinear algebra; matrix theory
Isosceles triangle theorem	Theorem	Geometry
Generating function for partitions	Theorem	Number theory
The nth roots of unity	Theorem	Number theory
Number of compositions	Theorem	Combinatorics
Scalar triple product	Proposition	Linear and multilinear algebra; matrix theory
Isomorphism with the coordinate space	Proposition	Linear and multilinear algebra; matrix theory
Partition of an interval	Concept	Real functions
Sum of a finite geometric series	Proposition	Sequences, series, summability
Expectation of a product of independent random variables	Theorem	Probability theory and stochastic processes
Space of solutions of a linear recurrence	Definition	Difference and functional equations
Stabilisers of points in the same orbit are conjugate	Proposition	Group theory and generalizations
Tangent function	Concept	Special functions
Determinant of a family of vectors in a basis	Concept	Linear and multilinear algebra; matrix theory
Left coset	Definition	Group theory and generalizations
Bounded sequence	Definition	Sequences, series, summability
Dimension	Definition	Linear and multilinear algebra; matrix theory
Inner automorphism group is isomorphic to G modulo its centre	Theorem	Group theory and generalizations
The rationals as the field of fractions of the integers	Example	Commutative algebra
Poincaré lemma for one-forms on convex sets	Theorem	Global analysis, analysis on manifolds
Angle sum of a triangle	Theorem	Geometry
Groups of prime order are cyclic	Corollary	Group theory and generalizations
Subgroup criterion	Proposition	Group theory and generalizations
Field generated by adjoining elements	Concept	Field theory and polynomials