an injective function. Factorization systems are a generalization of this situation in category theory. A factorization system (E, M) for a category C...

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

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...

morphism. A factorization system for a category also gives rise to a notion of embedding. If ( E , M ) {\displaystyle (E,M)} is a factorization system, then...

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

{\displaystyle (C\cap W,F)} is a weak factorization system, ( C , F ∩ W ) {\displaystyle (C,F\cap W)} is a weak factorization system W {\displaystyle W} satisfies...

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

equivalence class of such). In the presence of pullbacks and a proper factorization system, one can define the composition of relations. The composition X ←...

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

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

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...

algorithm, while that of model-based approaches is matrix factorization (recommender systems). A key advantage of the collaborative filtering approach...

Quillen. It is also used in the definition of a factorization system, and of a weak factorization system, notions related to but less restrictive than the...

on one's inference about the population mean. Fisher's factorization theorem or factorization criterion provides a convenient characterization of a sufficient...

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...

form of expressions: expanding products and powers, partial and full factorization, rewriting as partial fractions, constraint satisfaction, rewriting...

regular-epimorphisms and the monomorphisms form a factorization system. Every morphism f:X→Y can be factorized into a regular epimorphism e:X→E followed by...

is (normal epi, mono)-factorizable; in other words, the normal epimorphisms and the monomorphisms form a factorization system for the category. This...

Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. It uses only a small amount of space, and...

discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different...

A decision support system (DSS) is an information system that supports business or organizational decision-making activities. DSSs serve the management...

In number theory, the continued fraction factorization method (CFRAC) is an integer factorization algorithm. It is a general-purpose algorithm, meaning...

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

reason is that the factorization and stability is not a straightforward extension of the factorization and stability of 1-D systems because, for example...

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 =...

matching with the factorization labels in turn. Similarly add three more blocks 12CDEF, 34CDEF, and 56CDEF, replacing the factorization labels by the corresponding...

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

mapping which is tailored to matrix factorization algorithms. The basic idea is the following. A matrix factorization model represents the user-item interactions...

factorization of a morphism in a functorial way. In practice, it can be used to show some class of morphisms constitutes a weak factorization system in...