论文标题
两个完全共同地图的应用
Some applications of two completely copositive maps
论文作者
论文摘要
线性地图$φ：\ mathbb {m} _n \ to \ mathbb {m} _k $，如果结果矩阵$ [φ（a_ {j，i}）_ {i，j = 1}^m $对于任何inte inteeger $ $ m m $ m m $ m $ m $ m $ m $ m $，则称为完全共配。 $ [a_ {i，j}] _ {i，j = 1}^m $。在本文中，我们介绍了完全共同的映射$φ（x）=（\ mathrm {tr} x）i+x $和$ψ（x）=（\ mathrm {tr} x）i-x $。一些关于痕迹的痕迹不平等的新扩展包括$ 3 \ times 3 $块矩阵。
A linear map $Φ:\mathbb{M}_n \to \mathbb{M}_k$ is called completely copositive if the resulting matrix $[Φ(A_{j,i})]_{i,j=1}^m$ is positive semidefinite for any integer $m$ and positive semidefinite matrix $[A_{i,j}]_{i,j=1}^m$. In this paper, we present some applications of the completely copositive maps $Φ(X)=(\mathrm{tr} X)I+X$ and $Ψ(X)= (\mathrm{tr} X)I-X$. Some new extensions about traces inequalities of positive semidefinite $3\times 3$ block matrices are included.
