Matrix's triangular decomposition and its application

Matrix's triangular decomposition(LU decomposition) is the simplest and most basic kind of decomposition in matrix decomposition.In this paper,the theoretical analysis of matrix's triangular decomposition is mainly discussed,including such as the necessary and sufficient condition of uniqueness of existence in matrix's triangular decomposition and so on.And three special kind of triangular decomposition is introduced.In addition,the calculation of matrix' s triangular decomposition and the application on matrix' s triangular decomposition are detailedly discussed.At last a meaningful decomposition of simple polynomial matrix is drawn as a special example in this paper.