1,733 articles
Non-unique factorization
Non-unique factorization is the phenomenon in rings of algebraic integers and factorization monoids where an element has essentially different irreducible factorizations, classically 6 = 2·3 = (1+√−5)(1−√−5) in Z[√−5], measured by invariants like elasticity.
Noncommutative integration
Noncommutative integration is a branch of operator algebra theory extending measure and integration theory to von Neumann algebras, reducing to classical integration when the algebra is abelian.
Nonstandard analysis
Nonstandard analysis is a rigorous formulation of mathematical analysis using actual infinitesimal and infinitely large numbers instead of epsilon-delta limits, introduced by Abraham Robinson at Princeton in 1960.
Norm (mathematics)
In mathematics, a norm, or vector norm, is a function on a vector space that assigns each vector a length, satisfying positivity, homogeneity, and the triangle inequality.
Norm of a field element
The norm of a field element, N of alpha, is the determinant of the multiplication-by-alpha map for a finite field extension, taking values in the base field K.
Normal extension
A normal extension is an algebraic field extension E/F in which every irreducible polynomial over F with a root in E has all its roots in E; together with separability, normality makes the extension Galois.
Normal matrix
A normal matrix is a square matrix that commutes with its conjugate transpose, AA = A*A; by the spectral theorem it has an orthonormal basis of eigenvectors, including Hermitian and unitary matrices.
Normal subgroup
A normal subgroup, also called an invariant subgroup, is a subgroup H of a group G with aH = Ha for every element, equivalently fixed under conjugation by all of G.
Normed algebra
A normed algebra is an associative algebra equipped with a submultiplicative norm, meaning |ab| ≤ |a|·|b|; when the norm is complete it is called a Banach algebra.
Nth root
An nth root of a number a is a number b satisfying b^n = a; over the reals, odd roots of negatives are real while even roots are not.
Nuclear dimension
Nuclear dimension is a numerical invariant of C-algebras, introduced by Wilhelm Winter and Joachim Zacharias in 2009 as a noncommutative version of topological covering dimension.
Number
A number is a mathematical object used to count, measure, and label, built up in nested systems from the natural numbers to the integers, rationals, reals, and complex numbers.
Number field
A number field is a subfield of the complex numbers that is a finite extension of the rational numbers, and the central object of algebraic number theory.
Number of the beast
The number of the beast, also called the beast number (Greek: Χξς), is 666, given in Revelation 13:18 as the number of a beastly figure who forces everyone to receive a mark.
Number theory
Number theory, also called the theory of numbers or higher arithmetic, is the branch of mathematics studying the integers, primes, divisibility, and equations solved in whole numbers.
Number-theoretic transform
The number-theoretic transform (NTT) is a discrete Fourier transform computed modulo a prime instead of over the complex numbers, giving exact convolution for polynomial multiplication and cryptography.
Numeral system
A numeral system, also called a scale of notation, is a system for representing numbers using digits and rules for combining them, either additively or by place value.
Numerical algebraic geometry
Numerical algebraic geometry (NAG) is a tool set for approximating solutions to polynomial equation systems using numerical algorithms, initiated by Andrew Sommese and Charles Wampler.
Numerical stability
Numerical stability is the property of an algorithm whose rounding errors and small input perturbations do not grow unboundedly, central to scientific computing and numerical linear algebra.
NumPy
NumPy, or Numerical Python, is the primary open-source array programming library for Python, first released in 2006 and serving as the foundation of the scientific Python ecosystem.
Octal
Octal, also known as base 8, is the numeral system using the digits 0 through 7, where each digit corresponds to three binary bits, used in Unix file permissions.
Octonion
Octonions, also known as Cayley numbers, form an 8-dimensional normed division algebra over the real numbers, described by John Graves in 1843 and published by Arthur Cayley in 1845.
Octonions
The octonions, also known as Cayley numbers or octaves, are an eight-dimensional number system whose multiplication is neither commutative nor associative, the largest of the four normed division algebras.
On-Line Encyclopedia of Integer Sequences
The On-Line Encyclopedia of Integer Sequences (OEIS), also called Sloane's OEIS, is a free online database of integer sequences, online since 1996 and holding over 400,000 entries.
Ones' complement
Ones' complement is a method of representing signed integers in binary in which a negative number is formed by inverting every bit, used by early computers like the CDC 6600 and PDP-1.
OpenBLAS
OpenBLAS is an open-source, optimized implementation of the Basic Linear Algebra Subprograms (BLAS), based on Goto's GotoBLAS2 and including LAPACK, with hand-tuned assembly kernels for many CPU architectures.
Operand
An operand is the number, variable, or data that an operator acts on in mathematics or computing, as in 7 + 5, where 7 and 5 are operands.
Operation (mathematics)
In mathematics, an operation is a function that takes a fixed number of elements of a set as inputs and returns one element of the same set.
Operator K-theory
Operator K-theory is the branch of K-theory assigning K₀ and K₁ groups to C-algebras through projections and unitaries, central to classification and topological phases of matter.
Operator space theory
Operator space theory studies Banach spaces embedded in C-algebras, where matrix-level norms distinguish spaces that look identical as Banach spaces, merging C-algebra and Banach space theory.