Augustus Acevedo

2022-07-15

Consider $U=\left[{u}_{1}...{u}_{N}\right]$ to be a non-singular square matrix. I am interested in range space of $U$ but with one caveat, I want to find all $a$ such that each element of $Ua$ is non-negative. In other words for all natural basis vectors ${e}_{i}$
$0\le {e}_{i}^{T}Ua,\mathrm{\forall }i$
Is there a non-graphical, non-numerical approach that I can take to obtain all possible $a$?

Jamarcus Shields

Expert

Let

Since the matrix $U$ is non-singular,

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