Editing Factorization (section)

==Matrices==

Matrix rings are non-commutative and have no unique factorization: there are, in general, many ways of writing a [[matrix (mathematics)|matrix]] as a product of matrices. Thus, the factorization problem consists of finding factors of specified types. For example, the [[LU decomposition]] gives a matrix as the product of a [[lower triangular matrix]] by an [[upper triangular matrix]]. As this is not always possible, one generally considers the "LUP decomposition" having a [[permutation matrix]] as its third factor.

See [[Matrix decomposition]] for the most common types of matrix factorizations.

A [[logical matrix]] represents a [[binary relation]], and [[matrix multiplication]] corresponds to [[composition of relations]]. Decomposition of a relation through factorization serves to profile the nature of the relation, such as a [[difunctional]] relation.