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Let $A\in\mathbb{R}^{m \times n}$, $b\in\mathbb{R}^m$ such that $Ax\leq b$. Now let $\hat{x} = Tx$. What can be said about $A\hat{x}$? Concretely, is there an analytical way (without using $T^{-1}$) for computing a bound $\hat{b}$, such that $ATx\leq\hat{b}$?

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