example, 3 × 5 is an integer factorization of 15, and (x − 2)(x + 2) is a polynomial factorization of x2 − 4. Factorization is not usually considered meaningful...

called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer...

An RRQR factorization or rank-revealing QR factorization is a matrix decomposition algorithm based on the QR factorization which can be used to determine...

non-negative matrix factorizations was performed by a Finnish group of researchers in the 1990s under the name positive matrix factorization. It became more...

In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of...

algebra, an incomplete LU factorization (abbreviated as ILU) of a matrix is a sparse approximation of the LU factorization often used as a preconditioner...

Stein factorization, introduced by Karl Stein (1956) for the case of complex spaces, states that a proper morphism of schemes can be factorized as a composition...

fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can...

an LDU (factorization with all diagonal entries of L and U equal to 1), then the factorization is unique. In that case, the LU factorization is also unique...

Matrix factorization is a class of collaborative filtering algorithms used in recommender systems. Matrix factorization algorithms work by decomposing...

Integer factorization is the process of determining which prime numbers divide a given positive integer. Doing this quickly has applications in cryptography...

In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite...

and particularly in the field of complex analysis, the Weierstrass factorization theorem asserts that every entire function can be represented as a (possibly...

In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field...

unique factorization domains ⊃ principal ideal domains ⊃ euclidean domains ⊃ fields ⊃ algebraically closed fields Formally, a unique factorization domain...

it is a proper factorization of N. Each odd number has such a representation. Indeed, if N = c d {\displaystyle N=cd} is a factorization of N, then N =...

decimal digits (330 bits). Its factorization was announced on April 1, 1991, by Arjen K. Lenstra. Reportedly, the factorization took a few days using the multiple-polynomial...

circuits. In 2012, the factorization of 15 {\displaystyle 15} was performed with solid-state qubits. Later, in 2012, the factorization of 21 {\displaystyle...

Wheel factorization is a method for generating a sequence of natural numbers by repeated additions, as determined by a number of the first few primes...

factorization of a symmetric positive definite matrix is a sparse approximation of the Cholesky factorization. An incomplete Cholesky factorization is...

although there are many different ways of finding a factorization using an integer factorization algorithm, they all must produce the same result. Primes...

In algebraic topology and category theory, factorization homology is a variant of topological chiral homology, motivated by an application to topological...

In finite group theory, a branch of mathematics, a Thompson factorization, introduced by Thompson (1966), is an expression of some finite groups as a...

In number theory, an aurifeuillean factorization, named after Léon-François-Antoine Aurifeuille, is factorization of certain integer values of the cyclotomic...

elliptic-curve factorization or the elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer factorization, which...

integers, or, more generally, over a unique factorization domain (that is, a ring that has a unique factorization property similar to the fundamental theorem...

mathematics, a noncommutative unique factorization domain is a noncommutative ring with the unique factorization property. The ring of Hurwitz quaternions...

In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a way of finding a set of two...

\mathbb {F} ^{m\times n}} , a rank decomposition or rank factorization of A is a factorization of A of the form A = CF, where C ∈ F m × r {\displaystyle...

– Factorization of Mersenne numbers Mn (n up to 1280) Factorization of completely factored Mersenne numbers The Cunningham project, factorization of...