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Applied Mathematics-A Journal of Chinese Universities  2020, Vol. 35 Issue (2): 127-140    DOI: 10.1007/s11766-020-3617-1
    
The realization of positive definite matrices via planar networks and mixing-type sub-cluster algebras#br#
Diana Ahmad, YANG Yi-chao
Department of Mathematics, Zhejiang University (Yuquan Campus), Hangzhou 310027, China. Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China.
The realization of positive definite matrices via planar networks and mixing-type sub-cluster algebras
Diana Ahmad, YANG Yi-chao
Department of Mathematics, Zhejiang University (Yuquan Campus), Hangzhou 310027, China. Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China.
 全文: PDF 
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 definite matrix;  generalized Jacobi matrix;  planar network;  double wiring diagram;  cluster subalgebras    
Abstract: 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.
Key words: positive definite matrix    generalized Jacobi matrix    planar network    double wiring diagram    cluster subalgebras
出版日期: 2020-07-06
CLC:  15B48  
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引用本文:

Diana Ahmad, YANG Yi-chao. The realization of positive definite matrices via planar networks and mixing-type sub-cluster algebras#br#[J]. Applied Mathematics-A Journal of Chinese Universities, 2020, 35(2): 127-140.

Diana Ahmad, YANG Yi-chao. The realization of positive definite matrices via planar networks and mixing-type sub-cluster algebras. Applied Mathematics-A Journal of Chinese Universities, 2020, 35(2): 127-140.

链接本文:

http://www.zjujournals.com/amjcub/CN/10.1007/s11766-020-3617-1    或    http://www.zjujournals.com/amjcub/CN/Y2020/V35/I2/127

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