Factorization of a Matrix by the Elements of its Row Space

Factorization of a matrix is a means by which the regularity and order in phenomena can be discerned. Factorization of a matrix can be used in applications relevant to various scientific and policy concerns, we can mention here some examples of different uses for matrix factorization, although many of these uses overlap, so we can mention, interdependency and pattern delineation, parsimony or data reduction, discovering the basic structure of a domain. As a case in point, a scientist may want to uncover the primary independent lines or dimensions--such as size, leadership, and age--of variation in group characteristics and behavior, data collected on a large sample of groups and factorization can help disclose this structure. So factorization of a matrix is a fundamental theme in linear Algebra and applied statistics which has both scientific and engineering significance. In this paper we give a simple way for to factorize a matrix and we propose an algorithm with which we can factorize a matrix using some vectors of its row space.