Factorization

A factorization is in mathematics, the decomposition of an object into several non-trivial factors.

Examples of use:

• The always unique prime factorization of a natural number (see the factorization to obtain a factorization ).
• Algebraic terms can be often by factoring out the application and binomial formulas factoring.
• Polynomials can be factored. Over an algebraically complete body there are even getting a factorization into linear factors.
• A matrix can be decomposed into factors, which will (also known as LU or LU decomposition ), for example in solving systems of linear equations by means of triangular decomposition applied. The LU decomposition is in the numerical practice usually obtained with the Gaussian elimination.
• Another Matrizenfaktorisierung from the numerics is the QR decomposition, which can usually be obtained by means of Householder transformations or Givens rotations.
• Abstract attempts are made to break down the elements of wrestling into elementary factors. Nebenzahl, polynomial and matrix can be also the operator rings.
• In probability theory is called factorization, the decomposition of a random variable into independent summands, since the characteristic function of a sum of independent random variables is the product of the individual characteristic functions.
• The statistical factor analysis according to Spearman.
• The factorization of a logical proposition in relation to another proposition:

• In graph theory is called the decomposition of a graph G into subgraphs F, in which each node x only a certain number of a neighboring node has, as factorization, and its result as a- factors, eg 1- factors.