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.
基金
supported by National Natural Science Foundation of China(Grant No.11171217)
关键词
正矩阵
聚丙烯
矩阵对
P矩阵
分解
partially positive matrices
completely positive matrices
A-truncated K-moment problem
semidefinite algorithm
