# Definitions for **Factorization**

### This page provides all possible meanings and translations of the word **Factorization**

### Princeton's WordNet

factorization, factorisation, factoring(noun)

(mathematics) the resolution of an entity into factors such that when multiplied together they give the original entity

### Wiktionary

factorization(Noun)

: The process of creating a list of factors.

factorization(Noun)

: An expression listing items that, when multiplied together, will produce a desired quantity.

factorization(Noun)

A list of factors.

### Freebase

Factorization

In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x² − 4 factors as. In all cases, a product of simpler objects is obtained. The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viète's formulas relate the coefficients of a polynomial to its roots. The opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms. Integer factorization for large integers appears to be a difficult problem. There is no known method to carry it out quickly. Its complexity is the basis of the assumed security of some public key cryptography algorithms, such as RSA. A matrix can also be factorized into a product of matrices of special types, for an application in which that form is convenient. One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types: QR decomposition, LQ, QL, RQ, RZ.

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