Every idea

Ideas 451–600 of 7806.

Name	Kind	Subject
Determinant is multiplicative	Theorem	Linear and multilinear algebra; matrix theory
Correlation coefficient	Definition	Statistics
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
Inverse hyperbolic functions	Definition	Special functions
Order of a group is the index times the order of the subgroup	Theorem	Group theory and generalizations
Modular exponentiation	Concept	Number theory
Natural logarithm	Concept	Special functions
Commutativity	Definition	General algebraic systems
Circle group	Object	Topological groups, Lie groups
Spectrum of a matrix	Definition	Linear and multilinear algebra; matrix theory
Uniqueness of the supremum	Proposition	Order, lattices, ordered algebraic structures
Modulo operation	Definition	Number theory
Mesh of a partition	Definition	Real functions
Divisibility in a commutative ring	Definition	Commutative algebra
Riesz representation theorem in finite dimensions	Theorem	Functional analysis
Separation axioms	Concept	General topology
Divisor function	Concept	Number theory
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
Hockey-stick identity	Theorem	Combinatorics
Infimum	Definition	Order, lattices, ordered algebraic structures
Homogeneous system of linear equations	Concept	Linear and multilinear algebra; matrix theory
Clique number	Concept	Combinatorics
Sum of two squares theorem	Theorem	Number theory
Continued fraction	Concept	Number theory
Geometric distribution	Concept	Probability theory and stochastic processes
Lyapunov function	Definition	Ordinary differential equations
Almost sure convergence	Definition	Probability theory and stochastic processes
Index of a subgroup	Definition	Group theory and generalizations
Dedekind cut	Definition	Real functions
Euler's formula	Theorem	Special functions
Classification of discontinuities	Concept	Real functions
Cyclic groups are abelian	Proposition	Group theory and generalizations
Law of total expectation	Theorem	Probability theory and stochastic processes
Zorn's lemma	Theorem	Mathematical logic and foundations
Parabola	Concept	Geometry
Product topology on an arbitrary product	Definition	General topology
Doubling the cube	Problem	Geometry
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
Definite integral	Concept	Real functions
Little o notation	Definition	Approximations and expansions
Continued fraction expansion of a real number	Concept	Number theory
P-adic valuation	Definition	Number theory
Random walk	Concept	Probability theory and stochastic processes
Multiplicativity of the divisor function	Theorem	Number theory
Sigma-algebra	Definition	Measure and integration
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
Elementary row operations	Concept	Linear and multilinear algebra; matrix theory
Probability density function	Definition	Probability theory and stochastic processes
Monotone functions are Riemann integrable	Theorem	Real functions
Comparison test	Theorem	Sequences, series, summability
Tautology	Concept	Mathematical logic and foundations
Cardinality of a finite set	Definition	Mathematical logic and foundations
Harmonic conjugate	Concept	Potential theory
Symmetric group	Concept	Group theory and generalizations
The real numbers are uncountable	Theorem	Mathematical logic and foundations
Classical definition of probability	Concept	Probability theory and stochastic processes
Euclid's lemma	Lemma	Number theory
Product of a matrix and its adjugate	Theorem	Linear and multilinear algebra; matrix theory
Graph homomorphism	Concept	Combinatorics
Annihilating polynomial	Definition	Linear and multilinear algebra; matrix theory
Irreducible element	Definition	Commutative algebra
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
The dihedral group of order 8	Example	Group theory and generalizations
Complex exponential	Definition	Special functions
Sesquilinear form	Concept	Linear and multilinear algebra; matrix theory
Fermat numbers are pairwise coprime	Theorem	Number theory
PID implies UFD	Theorem	Commutative algebra
Perpendicular bisector	Concept	Geometry
Lipschitz condition	Definition	Real functions
Sequential continuity	Concept	Real functions
Jordan measure	Definition	Measure and integration
Lebesgue's criterion for Riemann integrability	Theorem	Real functions
Pointwise convergence	Definition	Sequences, series, summability
A matrix is diagonalisable iff it has a basis of eigenvectors	Theorem	Linear and multilinear algebra; matrix theory
Isosceles triangle theorem	Theorem	Geometry
Parametrised surface	Definition	Differential geometry
Generating function for partitions	Theorem	Number theory
The nth roots of unity	Theorem	Number theory
Number of compositions	Theorem	Combinatorics
Binary operation	Definition	General algebraic systems
Ptolemy's theorem	Theorem	Geometry
Scalar triple product	Proposition	Linear and multilinear algebra; matrix theory
Isomorphism with the coordinate space	Proposition	Linear and multilinear algebra; matrix theory
Probability measure	Concept	Probability theory and stochastic processes
Partition of an interval	Concept	Real functions
Sum of a finite geometric series	Proposition	Sequences, series, summability
Normal distribution	Concept	Probability theory and stochastic processes
Binary relation	Concept	Mathematical logic and foundations
Expectation of a product of independent random variables	Theorem	Probability theory and stochastic processes
Partial derivative	Definition	Real functions
Jump discontinuity	Definition	Real functions
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
Boundary	Concept	General topology
Zeckendorf's theorem	Theorem	Number theory
Pascal's triangle	Object	Combinatorics
Closed ball	Definition	General topology
Having a directional derivative	Definition	Real functions
Vector space	Definition	Linear and multilinear algebra; matrix theory
Left coset	Definition	Group theory and generalizations
Polarisation identity	Proposition	Functional analysis
Bounded sequence	Definition	Sequences, series, summability
Likelihood function	Definition	Statistics
Dimension	Definition	Linear and multilinear algebra; matrix theory
Union of a family of sets	Definition	Mathematical logic and foundations
T1 space	Definition	General topology
Homeomorphism	Definition	General topology
Root test	Theorem	Sequences, series, summability
Dihedral angle	Concept	Geometry
Dot product	Definition	Linear and multilinear algebra; matrix theory
Inner automorphism group is isomorphic to G modulo its centre	Theorem	Group theory and generalizations
Transitive closure	Concept	Mathematical logic and foundations
The rationals as the field of fractions of the integers	Example	Commutative algebra
Improper integral	Concept	Real functions
Limit of a sequence	Concept	Sequences, series, summability
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
Cross-ratio	Definition	Functions of a complex variable
Subgroup criterion	Proposition	Group theory and generalizations
Field generated by adjoining elements	Concept	Field theory and polynomials
Composition of continuous maps is continuous	Proposition	General topology
Eulerian trail	Concept	Combinatorics
Mean squared error	Concept	Statistics
Derivative of arctangent	Proposition	Special functions
Markov's inequality	Theorem	Probability theory and stochastic processes
Matrix of a composition is the product of matrices	Theorem	Linear and multilinear algebra; matrix theory
Orthogonal family for a bilinear form	Definition	Linear and multilinear algebra; matrix theory
Family of sets	Definition	Mathematical logic and foundations
Finitely generated module	Concept	Commutative algebra
Conservative vector field	Definition	Real functions
Additivity of the integral over intervals	Theorem	Real functions
Laplacian as a sum of second partial derivatives	Proposition	Partial differential equations
Number of edges of a complete graph	Proposition	Combinatorics