Every idea

Ideas 1201–1350 of 7806.

Name	Kind	Subject
Tangent plane and normal vector of a surface	Definition	Differential geometry
Spanning set	Definition	Linear and multilinear algebra; matrix theory
Subset	Concept	Mathematical logic and foundations
Mertens' theorem on Cauchy products	Theorem	Sequences, series, summability
Complex conjugate	Definition	Functions of a complex variable
Square root of a positive semidefinite matrix	Concept	Linear and multilinear algebra; matrix theory
Continued fraction	Definition	Number theory
Hölder's inequality for sums	Theorem	Real functions
Number of divisors	Definition	Number theory
Coordinate vector	Definition	Linear and multilinear algebra; matrix theory
Fermat's little theorem in the form a^p = a	Corollary	Number theory
Uniformly Cauchy sequence of functions	Concept	Sequences, series, summability
Line	Definition	Geometry
Trees are bipartite	Proposition	Combinatorics
Polynomial of an endomorphism	Definition	Linear and multilinear algebra; matrix theory
Trivial group	Example	Group theory and generalizations
Universal set	Definition	Mathematical logic and foundations
Eigenvalue	Concept	Linear and multilinear algebra; matrix theory
Permutation	Definition	Combinatorics
Quotient space	Concept	Linear and multilinear algebra; matrix theory
Side-side-side congruence	Theorem	Geometry
Goursat's theorem	Theorem	Functions of a complex variable
Inverse element	Definition	General algebraic systems
Polar form	Theorem	Functions of a complex variable
Quotient rule	Theorem	Real functions
Multiplication rule	Proposition	Probability theory and stochastic processes
Additive group of integers	Example	Group theory and generalizations
Set	Concept	Mathematical logic and foundations
Dense set	Concept	General topology
Z[√-5] is not a UFD	Counterexample	Number theory
Riemann's theorem on removable singularities	Theorem	Functions of a complex variable
Polar coordinates	Concept	Geometry
Squaring the circle	Problem	Geometry
Minor	Concept	Linear and multilinear algebra; matrix theory
Supremum	Definition	Order, lattices, ordered algebraic structures
Borel sigma-algebra	Definition	Measure and integration
Trajectory	Definition	Dynamical systems and ergodic theory
Pythagorean theorem in an inner product space	Theorem	Functional analysis
Matrix addition	Definition	Linear and multilinear algebra; matrix theory
Antiderivative	Definition	Real functions
Characteristic polynomial of a linear recurrence	Definition	Difference and functional equations
Bias of an estimator	Concept	Statistics
Uniform limits commute with integration	Theorem	Sequences, series, summability
Box topology	Concept	General topology
Power series converge uniformly on smaller discs inside the radius of convergence	Theorem	Functions of a complex variable
Ring of integers	Theorem	Commutative algebra
Implicit function theorem	Theorem	Real functions
Having a gradient	Definition	Real functions
Minimal element	Concept	Order, lattices, ordered algebraic structures
Cantor set	Example	General topology
Complete metric space	Concept	General topology
Slopes of a convex function are increasing	Proposition	Real functions
Generalized pigeonhole principle	Theorem	Combinatorics
Least squares	Concept	Numerical analysis
Antiderivative	Concept	Real functions
Clique	Concept	Combinatorics
Zero derivative on a connected open set implies constant	Theorem	Real functions
Characteristic polynomial of a linear map	Definition	Linear and multilinear algebra; matrix theory
Addition rule for two events	Proposition	Probability theory and stochastic processes
Order of the dihedral group	Proposition	Group theory and generalizations
Recurrence for Stirling numbers of the second kind	Theorem	Number theory
Laplace expansion along a row	Theorem	Linear and multilinear algebra; matrix theory
Random walk	Definition	Probability theory and stochastic processes
Simple group	Definition	Group theory and generalizations
Separately continuous but not continuous function	Counterexample	Real functions
Density of the normal distribution	Concept	Probability theory and stochastic processes
Linear maps on finite-dimensional spaces are continuous	Theorem	Operator theory
pi	Object	Number theory
Finite extension	Concept	Field theory and polynomials
Family of sets	Concept	Mathematical logic and foundations
Random variable with a density	Definition	Probability theory and stochastic processes
Rectifiable curve	Definition	Real functions
Hamiltonian system	Definition	Dynamical systems and ergodic theory
Determinant is the product of the eigenvalues	Theorem	Linear and multilinear algebra; matrix theory
Dual map	Definition	Linear and multilinear algebra; matrix theory
Associativity of addition	Theorem	Mathematical logic and foundations
Interior	Definition	General topology
Determinant	Definition	Linear and multilinear algebra; matrix theory
Euler product formula	Theorem	Number theory
Monic polynomial	Concept	Commutative algebra
Integers	Object	Number theory
Eigenvalues of a self-adjoint operator are real	Theorem	Operator theory
Bernstein polynomial	Definition	Approximations and expansions
Inclusion–exclusion for two sets	Theorem	Combinatorics
Recurrence for Stirling numbers of the first kind	Theorem	Number theory
Chromatic number	Definition	Combinatorics
Hyperbolic equilibrium point	Definition	Ordinary differential equations
Number of subsets of a finite set	Theorem	Combinatorics
Codomain	Concept	Mathematical logic and foundations
Polynomial functions are continuous	Proposition	Real functions
Multigraph	Concept	Combinatorics
Uncorrelated random variables that are not independent	Counterexample	Probability theory and stochastic processes
Tangent line to a circle	Definition	Geometry
Cartesian product	Definition	Mathematical logic and foundations
Normal operator	Concept	Operator theory
Möbius function	Definition	Number theory
Greatest common divisor	Concept	Number theory
Euclidean distance	Definition	Geometry
Contractive sequence	Concept	Sequences, series, summability
Rooted tree	Definition	Combinatorics
Altitude of a triangle	Concept	Geometry
Reverse triangle inequality	Corollary	Real functions
The kernel is a normal subgroup	Proposition	Group theory and generalizations
Sequential compactness	Definition	General topology
Normal subgroup	Concept	Group theory and generalizations
Complex numbers as pairs of reals	Concept	Functions of a complex variable
Kurtosis	Definition	Statistics
Normal extension	Definition	Field theory and polynomials
Logistic equation	Example	Biology and other natural sciences
Harmonic conjugate	Definition	Potential theory
Discriminant of a polynomial	Definition	Field theory and polynomials
Matrix–vector product	Definition	Linear and multilinear algebra; matrix theory
Two-sided ideal	Concept	Associative rings and algebras
A finite field of order q is the splitting field of x^q - x	Theorem	Field theory and polynomials
Riemann sphere	Definition	Functions of a complex variable
Degrees along an Eulerian trail	Theorem	Combinatorics
Martingale	Definition	Probability theory and stochastic processes
Universal property of the free group	Theorem	Group theory and generalizations
Work done by a force field	Concept	Real functions
Arctangent	Concept	Special functions
Conic section	Definition	Geometry
Number of permutations	Theorem	Combinatorics
Modular multiplicative inverse	Concept	Number theory
Zero of a holomorphic function	Definition	Functions of a complex variable
Polynomials in several variables	Definition	Commutative algebra
Classification of complex quadratic forms	Theorem	Number theory
exp(2 pi i/n) is a primitive root of unity	Proposition	Number theory
Frobenius automorphism of a finite field	Concept	Field theory and polynomials
Special orthogonal group	Object	Linear and multilinear algebra; matrix theory
Disc of convergence	Concept	Functions of a complex variable
Irreducible elements need not be prime	Counterexample	Commutative algebra
Division algorithm	Theorem	Number theory
Subbasis	Definition	General topology
Euclidean domain	Concept	Commutative algebra
Finite subgroups of the multiplicative group of a field are cyclic	Theorem	Field theory and polynomials
Cyclic quadrilateral	Definition	Geometry
Principal ideal domain	Concept	Commutative algebra
Equivalent matrices	Concept	Linear and multilinear algebra; matrix theory
Abel's test	Theorem	Sequences, series, summability
Topological space	Definition	General topology
First-countable space	Concept	General topology
Square matrix	Definition	Linear and multilinear algebra; matrix theory
Impossibility of doubling the cube	Theorem	Field theory and polynomials
Absolute value is continuous but not differentiable at 0	Counterexample	Real functions
Topological space	Concept	General topology
Bernoulli process	Concept	Probability theory and stochastic processes
Parabola	Definition	Geometry
Linear independence	Concept	Linear and multilinear algebra; matrix theory
Uniform convergence of derivatives allows term-by-term differentiation	Theorem	Sequences, series, summability
Exponential growth beats polynomial growth	Theorem	Real functions