Given the matrix $(\sum_{i=1}^{n}A^{T}_{i}+A_i)$ is negative-definite, is it possible to derive any conclusion about the definiteness of $A_i+A^{T}_{i}$ for $i=1,2,\cdots,n$?
2026-03-25 14:35:52.1774449352
What can be said about the definiteness of $A^{T}_i+A_i$ when $\sum_{i=1}^{n}A^{T}_{i}+A_i<0$?
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No. Consider $n=2$, $A_1=[-2]$, $A_2=[1]$.