Suppose we are multiplying matrix $A$ with a diagonal matrix $D$ from left, i.e.,

$X=D A$

where $D$ is a diagonal matrix with elements

$$d_{ii}=\frac{1}{2} \text{ for } i=1,n$$

$$d_{ii}=\frac{1}{3} \text{ for } i =2, \dots, n-1.$$

Is there any relation with the set of eigenvalues of $X$ and $A$ (like any lower bounds on the eigenvalues)?