Partially positive matrices  

作　　者：ZHOU AnWa FAN JinYan 

机构地区：[1]Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University

出　　处：《Science China Mathematics》2015年第10期2245-2254,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11171217)

摘　　要：A real n × n symmetric matrix P is partially positive(PP) for a given index set I ? {1,..., n} if there exists a matrix V such that V(I, :) 0 and P = V VT. We give a characterization of PP-matrices. A semidefinite algorithm is presented for checking whether a matrix is partially positive or not. Its properties are studied. A PP-decomposition of a matrix can also be obtained if it is partially positive.A real n × n symmetric matrix P is partially positive（PP） for a given index set I ？ {1,..., n} if there exists a matrix V such that V（I, ：） 0 and P = V VT. We give a characterization of PP-matrices. A semidefinite algorithm is presented for checking whether a matrix is partially positive or not. Its properties are studied. A PP-decomposition of a matrix can also be obtained if it is partially positive.

关 键 词：partially positive matrices completely positive matrices A-truncated K-moment problem semidefinite algorithm 

分 类 号：O151.21[理学—数学] TQ325.14[理学—基础数学]