Category:Mathematical fact
This category is part of modular mathematics and is for facts, that is, statements known to be true. These include theorems, lemmas, corollaries and propositions.
Pages in category "Mathematical fact"
The following 200 pages are in this category, out of 495 total.
(previous page) (next page)A
- Affin-lineare mapping/Values on affine basis/Fact
- Affine space/Affine Basis/Barycentric coordinates/Fact
- Affine space/Affine basis/Hyperplane realization/Fact
- Affine space/Affine subspace/Characterization/Fact
- Affine space/Affine subspace/Intersection property/Fact
- Affine space/Finite point family/Affinely independent/Characterization/Fact
- Affine space/Point set/Barycentric combination/Point/Fact
- Affine space/Point set/Generated affine subspace/Fact
- Affine varieties/Under geometric deformation/Transcendental not affine, algebraic affine/Fact
- Affine-linear mapping/Barycentric combination/Fact
- Affine-linear mapping/Fixed point/Linear/Fact
- Affine-linear mapping/Functorial properties/Fact
- Alternating mapping/Swap property/Fact
- Angle bisector/Distance condition/Fact
B
- Base change/Three bases/Composition/Fact
- Basis/Dual basis/Tautological lemma/Fact
- Bijective group homomorphism/Inverse mapping/Homomorphism/Fact
- Bilinear form/Gram matrix under base change/Fact
- Bilinear form/Linear forms/Nondegenerate/Fact
- Bilinear form/Symmetric/Definiteness/Minor criterion/Fact
- Bilinear form/Symmetric/Eigenvalue criterion/Fact
- Bilinear form/Symmetric/Type/Inertia law/Fact
- Bilinear form/Symmetric/Type/Minor criterion/Fact
- Bilinear form/Via mapping to dual space/Fact
- Binomial coefficient/Sum in Pascal triangle/Fact
C
- Cathetus theorem/Linear algebra/Fact
- Cayley-Hamilton/Fact
- Cayley-Hamilton/Matrix version/Fact
- Cayley-Hamilton/Minimal polynomial and characteristic polynomial/Fact
- Characteristic polynomial/Coprime factorization/Direct sum/Fact
- Characteristic polynomial/Direct sum decomposition/Fact
- Circumcenter as origin/Sum of points on altitude/Fact
- Cohen-Macaulay graded ring/Positive characteristic/Parameter/Tight closure/Degree criterion/Inclusion/Fact
- Cohen-Macaulay ring/Positive characteristic/Cohomological criterion for tight closure/Fact
- Column stochastic matrix/Isometric with respect to sum norm/Fact
- Column stochastic matrix/Positive row/Convergence/Fact
- Column stochastic matrix/Positive row/One-dimensional eigenspace/Fact
- Column stochastic matrix/Stable/Fact
- Commutative ring/Ring homomorphism/Kernel/Ideal/Fact
- Compact interval/Real function/Riemann integrable on partition/Fact
- Compactness/Heine-Borel/Fact
- Complex Conjugation/Rules/Fact
- Complex numbers/Conjugation/Real part imaginary part/Fact
- Complex numbers/Field/Fact
- Complex numbers/Modulus/Rules/Fact
- Complex numbers/Real and imaginary part/Properties/Fact
- Congruent triangles/Same lengths/Fact
- Continuous function/Closed bounded interval/Maximum is attained/Fact
- Continuous Function/Primitive function exists/Fact
- Continuous function/R/Intermediate value theorem/0-version/Fact
- Continuous function/R/Intermediate value theorem/Fact
- Continuous mapping/Image of a compact space/Compact/Fact
- Convergent power series/R/Primitive function/Fact
- Convergent power series/R/Taylor series/Coincidence/Fact
- Cyclotomic equation over C/Explicit description/Fact
D
- Determinant function/Behavior under row operations/Fact
- Determinant function/Uniquely determined/Fact
- Determinant/Field/Upper triangular matrix/Fact
- Determinant/Laplace expansion/Fact
- Determinant/Leibniz formula/Fact
- Determinant/Multiplication theorem/Fact
- Determinant/Recursively/Alternating/Fact
- Determinant/Recursively/Alternating/Swap property/Fact
- Determinant/Recursively/Multilinear/Fact
- Determinant/Transposed matrix/Universal property/Fact
- Determinant/Zero, linear dependent and rank property/Fact
- Differentiable function/D in R/Chain rule/Fact
- Differentiable function/D in R/Continuity in point/Fact
- Differentiable function/D in R/Inverse function/Fact
- Differentiable function/D in R/Linear approximation/Fact
- Differentiable function/D in R/Rules/Fact
- Differentiable function/D open in K/Chain rule/Fact
- Differentiable function/D open in K/Rules/Fact
- Differentiable function/Mean value theorem/Quotient version/Fact
- Differentiable functions/Mean value theorem/Fact
- Direct sum/Linear mapping/Fact
- Divisibility theory (Z)/Lemma of Bezout/Fact
- Division with remainder/Z/Fact
- Dual mapping/Dual basis/Matrix/Fact
E
- Eigenspaces/Direct sum/Dimension/Fact
- Eigenvalues/Endomorphism/Matrix/Fact
- Eigenvalues/Endomorphism/Under Isomorphism/Fact
- Endomorphism/Characteristic polynomial/Different linear factors/Diagonalizable/Fact
- Endomorphism/Diagonalizable/Algebraic and geometric multiplicity/Fact
- Endomorphism/Eigenspaces are linear subspaces/Zero/Fact
- Endomorphism/Eigenvalue and characteristic polynomial/Fact
- Endomorphism/Eigenvalue/Invariant hyperplane/Fact
- Endomorphism/Eigenvectors/Linearly independent/Fact
- Endomorphism/Finite-dimensional/Minimal polynomial/Principal ideal/Fact
- Endomorphism/Generalized eigenspace/Algebraic multiplicity/Fact
- Endomorphism/Geometric and algebraic multiplicity/Fact
- Endomorphism/Invariant linear subspace/Minimal polynomial/Divisibility/Fact
- Endomorphism/Invariant linear subspace/Polynomial/Action/Fact
- Endomorphism/K/Power/Decomposition/Fact
- Endomorphism/K/Powers/Boundedness/Fact
- Endomorphism/K/Powers/Convergence/Fact
- Endomorphism/K/Powers/Zero convergence/Fact
- Endomorphism/Polynomial/Eigenvector/Fact
- Endomorphism/Power sequence/Convergence/Eigenvector or 0/Fact
- Endomorphism/Real/Two-dimensional invariant/Fact
- Endomorphism/Trigonalizable/Canonical additive decomposition/Fact
- Endomorphism/Trigonalizable/Direct sum/Fact
- Endomorphismus/Finite dimensional/Change of basis/Fact
- Equivalence classes/Partition/Quotient set/Properties/Fact
- Equivalence relation/Quotient set/Universal property/Fact
- Euclidean plan/Proper isometry/Rotation/Fact
- Euclidean plane/Finite subgroup/Proper/Cyclic/Fact
- Euclidean plane/Improper isometry/Axis reflection/Fact
- Euclidean space/Affine subspace/Perpendicular/Fact
- Euclidean space/Distance to hyperplane/Linear form/Fact
- Euclidean space/Distance to subspace/Inner product/Fact
- Euclidean space/Distance to subspace/Orthogonal projection/Fact
- Euclidean space/Isometry/Structure/Fact
- Euclidean space/Linear form/Corresponding vector/Fact
- Euclidean vector space/Isometry with standard space/Fact
- Euclidean vector space/Isometry/Orthogonal/Fact
- Euclidean vector space/Linear mapping/Angle-preserving/Structure/Fact
- Euclidean vector space/R^3/Isometry/Eigenvector/Fact
- Euclidean vector space/R^3/Proper isometry/Fact
- Euclidean vector space/R^3/Proper isometry/Representation/Fact
- Exponential series/Real/Absolute convergence/Fact
- Exponential series/Real/Elementary properties/Fact
- Exponential series/Real/Functional equation/Fact
F
- Field extension/Vector space/Fact
- Field/Basic properties/Fact
- Field/Binomi/Fact
- Field/Domain/Fact
- Field/Two ideals/Fact
- Field/Uniqueness of negative and inverse element/Fact
- Finite field/Smooth projective curve/Vector bundel/Etale trivializable and Frobenius periodicity/Fact
- Finite field/Smooth projective curve/Vector bundle/Affineness and nonexistence of curves/Fact
- Finite field/Smooth projective curve/Vector bundle/Finite annihilation/Harder-Narasimhan-criterion/Fact
- Finite field/Smooth projective curve/Vector bundle/Strongly semistable degree 0/Trivializable/Fact
- Finite field/Smooth projective curve/Vector bundle/Strongly semistable degree nonnegative/Finite annihilation/Fact
- Finite permutation group/Cardinality/Fact
- Finite permutation/Representation with transpositions/Fact
- Finite subgroup/Isometry group/Affine/Common fixed point/Fact
- Finite symmetry group/Cube from numerical condition/Permutation group/Fact
- Finite symmetry group/Space/Classification/Fact
- Finite symmetry group/Tetrahedron from numerical condition/Fact
- Finite-dimensional vector space/Dual basis/Basis/Fact
- Finite-dimensional vector space/Linear mapping/Two generalized eigenspaces/Fact
- Finite-dimensional vector space/Linear subspace/Kernel/Solution space/Fact
- Forcing algebra/Primary ideal/Induced torsor/Fact
- Forcing algebra/Relation to tight closure/Local cohomology/Characterization/Fact
- Function/R/Limit/Epsilon/Characterizations/Fact
- Function/R/Limit/Epsilon/Rules/Fact
- Fundamental theorem of algebra/Nonconstant polynomial/Zero/Fact
- Fundamental theorem of calculus/Riemann/Fact
G
- Geometric series/Real/Convergence/Absolutely/Fact
- Group homomorphism/Categorial properties/Fact
- Group homomorphism/Factorization/Fact
- Group homomorphism/Homomorphism theorem/Surjective and kernel/Fact
- Group homomorphism/Image/Subgroup/Fact
- Group homomorphism/Injectivity and kernel/Fact
- Group homomorphism/Inverse to inverse/Fact
- Group homomorphism/Kernel/Normal subgroup/Fact
- Group homomorphism/Kernel/Subgroup/Fact
- Group homomorphism/Surjective and residue class group/Fact
- Group homomorphism/Z to group/Fact
- Group theory (algebra)/Lagrange's theorem/Fact
- Group theory/Cosets/Properties/Fact
- Group theory/Finite/Order/Different/Fact
- Group theory/Isomorphism theorem for residue class groups/Fact
- Group theory/Lagrange/Order of an element/Fact
- Group/Inverse element/Unique/Fact
- Group/Normal subgroup/Residue class group/Fact
H
- Hermitian form/Type via self-adjoint endomorphism/Fact
- Hilbert-Kunz multiplicity/Two-dimensional graded/Brenner-Trivedi-formula/Fact
- Hilbert-Kunz multiplicity/Two-dimensional graded/Formula for maximal ideal in plane case/Fact
- Hilbert-Kunz/Invariant ring/Coinvariants/Fact
- Hilbert-Kunz/Invariant ring/Coinvariants/Polynomial ring/Fact
- Hilbert-Kunz/Relative two-dimensional situation/Limit and interpretation/Fact
- Homogeneous linear system/Dimension estimate/Fact
- Homomorphism space/Bases/Matrices/Fact
- Homomorphism space/Dimension/Fact
- Homomorphism space/Direct sum decomposition/Fact
- Homomorphism space/Functorial properties/Fact
- Homomorphism space/Linear subspaces/Fact
- Hospital/Differentiable in inner interval/Fact
- Hyperbolic function/R/Monotonicity properties/Fact
- Hyperbolic functions/R/Elementary properties/Fact
- Hyperplane/Kernel of a linear form/Fact
I
- Inner automorphism/Automorphism/Fact
- Inner product/K/Cauchy-Schwarz/Fact
- Inner product/K/Norm/Properties/Fact
- Inner product/K/Polarization identity with norm/Fact
- Inner product/R/Cauchy-Schwarz/Fact
- Integration by parts/Fact
- Integration/Substitution/dx version/Fact
- Integration/Substitution/Fact
- Intercept theorem/Three rays/Fact
- Intercept theorem/Two rays/Fact
- Intercept theorem/Two rays/Similarity of triangles/Fact
- Interval/Continuous function/Riemann integrable/Fact
- Interval/Primitive function/Constant difference/Fact
- Inverse trigonometric functions/Derivative/Fact
- Invertible matrix/Finite order/C/Diagonalizable/Fact
- Invertible matrix/Staircase form/Identity matrix/Fact
- Isometry/C/Diagonalizable/Fact