论文标题
对称和非对角性非负实矩阵的光谱稀疏性范围
Bounds on the Spectral Sparsification of Symmetric and Off-Diagonal Nonnegative Real Matrices
论文作者
论文摘要
我们说，当其对角线以外的所有条目都是非负实数时，我们说一个方形真实矩阵$ m $ is \ emph {off-diagonal nonnondergative}。在本说明中，我们表明，对于任何非对抗的非负对称矩阵$ m $，存在一个非负对称矩阵$ \ widehat {m} $，该{m} $稀疏并且在频谱中均为$ m $。
We say that a square real matrix $M$ is \emph{off-diagonal nonnegative} if and only if all entries outside its diagonal are nonnegative real numbers. In this note we show that for any off-diagonal nonnegative symmetric matrix $M$, there exists a nonnegative symmetric matrix $\widehat{M}$ which is sparse and close in spectrum to $M$.
