论文标题
哈哈达姆第二等级的权力，双重的非负矩阵
Hadamard powers of rank two, doubly nonnegative matrices
论文作者
论文摘要
我们研究$ r \ textrm {th} $ hadamard douly非负矩阵的能力，并表明矩阵$ a^{\ circ r} $对于每个$ n \ times n $ dubly doubly nonnodengation nornodengative notengation n $ r> n-2 $ a $ and a $ a $ a a $ a a $ a a $ a a $ a a $ a a $ a a $ a a $ a a $ a a $ a n $ a a $ a n $ a a $ a a $ a的肯定是积极的。给予对六个等级级别的Hadamard权力的等级，阳性和单调性的研究，这些级别的阳性半足质矩阵具有所有条目。
We study ranks of the $r\textrm{th}$ Hadamard powers of doubly nonnegative matrices and show that the matrix $A^{\circ r}$ is positive definite for every $n\times n$ doubly nonnegative matrix $A$ and for every $r>n-2$ if and only if no column of $A$ is a scalar multiple of any other column of $A.$ A particular emphasis is given to the study of rank, positivity and monotonicity of Hadamard powers of rank two, positive semidefinite matrices that have all entries positive.
