Pascal型矩阵和广义Pascal型矩阵  

PASCAL TYPE MATRICES AND GENERALIZED PASCAL TYPE MATRICES

作　　者：黄凤英[1] 柳柏濂[1] 

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《华南师范大学学报（自然科学版）》2008年第1期6-12,共7页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10331020)

摘　　要：把Pascal型矩阵Pn,l推广到另一类Pascal型矩阵P*n,l,其中当i≥j时,[Pn,l]ij=ji--11++ll,[Pn*,l]ij=i-j1-1+l,并且当i<j时,[Pn,l]ij=[Pn*,l]ij=0.同时,得到了Pascal型矩阵的一些性质及它们的逆矩阵.另外还研究了一类广义Pascal型矩阵,证明了这类矩阵的Cholesky因子分解式的每个元都可以由超几何函数2F1(a,b;c;x)表出.The Pascal type matrix Pn,λ, is extended to another Pascal type matrix Pn,λ^＊,where [Pn,λ]ij=（i-1＋λ j-1＋λ）and [Pn,λ^＊]ij=（i-1＋λ j-1）as i≥j,and [Pn,λ]ij=[Pn,λ^＊]ij=0 as i 〈j. Some propositions and the inverse matrices of these Pascal type matrices are obtained. Moreover, a generalized Pascal type matrix is studied. It is shown that each entry of the Cholesky factorization Pn,λ^＊（x ,y）Pn,λ^＊ （x ,y）^T can be represented by the hypergeometric functions 2F1 （a,b,c;x）,where [Pn,λ^＊（x,y）]ij=x^i-j y^i＋j-2（i-1＋λ j-1） if i≥j,and [Pn,λ^＊（x,y）]ij=0 if i〈j.

关 键 词：Pascal型矩阵 Fibonacci型矩阵 Cholesky因子分解 超几何函数 

分 类 号：O157.5[理学—数学]