2014/06/26 by Fang Li, Li, Fang, Yichao Yang +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #05E15 #13F60 #15B48 #15B57 #Advanced Mathematical Theories and Applications #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.RA #msc:05E15 #msc:13F60 #msc:15B48 #msc:15B57
paper · pdf · doi:10.48550/arxiv.1406.6759
11 pages, 6 figures
arxiv created 2014/06/26 · openalex publication_date 2014/06/26 · arxiv updated 2014/06/27 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28
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.Zelevisky \cite[4], in this paper, we give the test method of positive definite matrices via the planar networks and the so-called cluster subalgebra 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 cluster subalgebras.