In math, factorization (British English: factorisation) or factoring is the decay of an entity (for example, a digit, a polynomial, or a matrix into a result of additional objects, or factors, which when multiplied jointly give the innovative. For example, the digit 15 factors into primes as 3 × 5, and the polynomial x2 - 4 parts as (x - 2)(x + 2). In all cases, a product of simpler objects is attained.
The aim of factoring is typically to decrease something to "essential construction blocks," such as facts to prime numbers, or polynomials to irreducible polynomials. Factoring integers is enclosed by the basic theorem of mathematics and factoring polynomials by the basic theorem of algebra.
The contradictory of factorization is development. This is the procedure of multiplying jointly factors to reconstruct the novel, "prolonged" polynomial.Integer factorizations for great integers come into view to be a hard problem. There is no known technique to carry it out rapidly. Its complication is the base of the assumed safety of some public key cryptography algorithms, as like RSA.
A matrix can furthermore be factorized into a product of matrices of particular forms, for a function in which that figures is suitable. One main example of this exercises an orthogonal or unitary matrix, and a triangular matrix. There are dissimilar kinds: QR decay, LQ, QL, RQ, RZ.
One more example is the factorization of a function as the composition of additional functions having positive possessions; for example, each function can be out looked as the composition of a subjective task with an injective task.
The aim of factoring is typically to decrease something to "essential construction blocks," such as facts to prime numbers, or polynomials to irreducible polynomials. Factoring integers is enclosed by the basic theorem of mathematics and factoring polynomials by the basic theorem of algebra.
The contradictory of factorization is development. This is the procedure of multiplying jointly factors to reconstruct the novel, "prolonged" polynomial.Integer factorizations for great integers come into view to be a hard problem. There is no known technique to carry it out rapidly. Its complication is the base of the assumed safety of some public key cryptography algorithms, as like RSA.
A matrix can furthermore be factorized into a product of matrices of particular forms, for a function in which that figures is suitable. One main example of this exercises an orthogonal or unitary matrix, and a triangular matrix. There are dissimilar kinds: QR decay, LQ, QL, RQ, RZ.
One more example is the factorization of a function as the composition of additional functions having positive possessions; for example, each function can be out looked as the composition of a subjective task with an injective task.
