  Let $G$ be a simple graph with adjacency matrix $A(G)$, signless Laplacian
matrix $Q(G)$, degree diagonal matrix $D(G)$ and let $l(G)$ be the line graph
of $G$. In 2017, Nikiforov defined the $A_\alpha$-matrix of $G$, $A_\alpha(G)$,
as a linear convex combination of $A(G)$ and $D(G)$, the following way,
$A_\alpha(G):=\alpha A(G)+(1-\alpha)D(G),$ where $\alpha\in[0,1]$. In this
paper, we present some bounds for the eigenvalues of $A_\alpha(G)$ and for the
largest and smallest eigenvalues of $A_\alpha(l(G))$. Extremal graphs attaining
some of these bounds are characterized.
