The Factorization Of The Pascal Matrix And The Riordan Matrix

Along with the rapid development of the computer and our country's science, matrix, as a kind of science research tools, is used more and more widely. The factorization theory of matrix is of great importance to the theory of matrix and numerical value calculation.It is to decompose a matrix into several rather simple matrixes through changes or a product of some matrix with certain special characters.In this paper, using the Fibonacci matrix and the Jacobsthal matrix, we factorize the Pascal matrix .The contents can be summarized as follows:In chapter I, we introduce the background of the factorization of the matrix, then give the preparation knowledge of the Pascal matrix.In chapterⅡ, using the Binomial coefficient, we introduce a new matrix R _n. Laying heavy stress on researching factorization of the Pascal matrix involving the Fibonacci matrix, finally we obtain simple decomposition type of the Pascal matrix.ChapterⅢcan be divided into three parts, first a new matrix R _n is introduced, from it we obtain a factorization Pn = RnJn that involving Pascal matrix,then factorize the matrix R _n and J_ n, finally obtain the decomposition type of the Pascal matrix.Chapter IV introduce one theory—Riordan matrix theory, point out its relationship with Pascal matrix, finally get some combinatorial identities.