I have an equality as follows

$$s^T\phi\leq -|s|^TA$$

where $s$, $\phi$ and $A$ are vectors with appropriate dimensions. I want to prove that this inequality holds for the following too

$$s^TM\phi\leq -|s|^TMA$$

where $M$ has positive eigenvalues. Intuitively, it seems to be right. Any ideas?

I have an inequality as follows

$$s^T\phi\leq -|s|^TA$$

where $s$, $\phi$ and $A$ are vectors with appropriate dimensions. I want to prove that this inequality holds for the following too

$$s^TM\phi\leq -|s|^TMA$$

where $M$ has positive eigenvalues. Intuitively, it seems to be right. Any ideas?