Summary: Let \(G\) be a graph with adjacency matrix \(A(G)\), and let \(D(G)\) be the diagonal matrix of the degrees of \(G\). The signless Laplacian \(Q(G)\) of \(G\) is defined as \(Q(G) :=A(G) +D(G)\). Cvetković called the study of the adjacency matrix the \(A\)-spectral theory, and the study of the signless Laplacian – the \(Q\)-spectral theory. To track the gradual change of \(A(G)\) into \(Q(G)\), in this paper it is suggested to study the convex linear combinations \(A_\alpha(G)\) of \(A(G)\) and \(D(G)\) defined by \[ A_\alpha (G) :=\alpha D(G) + (1-\alpha)A(G), \quad 0 \leq \alpha \leq 1. \] This study sheds new light on \(A(G)\) and \(Q(G)\), and yields, in particular, a novel spectral Turán theorem. Several open problems are discussed.