The realization of positive definite matrices via planar networks and mixing-type sub-cluster algebras  

作　　者：Diana Ahmad YANG Yi-chao 

机构地区：[1]Department of Mathematics,Zhejiang University(Yuquan Campus),Hangzhou 310027,China [2]Department of Mathematics,Changshu Institute of Technology,Changshu 215500,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2020年第2期127-140,共14页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11671350,11571173,11801043);Natural Science Foundation for Youths of Jiangsu Province(BK20181031).

摘　　要：As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevinsky[7],in this paper,we give a test method of positive definite matrices via the planar networks and the so-called mixing-type sub-cluster algebras respectively,introduced here originally.This work firstly gives a combinatorial realization of all matrices through planar network,and then sets up a test method for positive definite matrices by LDU-decompositions and the horizontal weightings of all lines in their planar networks.On the other hand,mainly the relationship is built between positive definite matrices and mixing-type sub-cluster algebras.

关 键 词：positive de nite matrix generalized Jacobi matrix planar network double wiring diagram cluster subalgebras 

分 类 号：O151.21[理学—数学]