I just started learning quantum physics and there is a particular notion confusing me.
While reading McIntyre book, he suggests I find the matrix representation of the $S_n$ operator, which is the operator for the spin component allong a general direction $\mathbf{\hat{n}}=\mathbf{\hat{i}}\sin\theta\cos\phi+\mathbf{\hat{j}}\sin\theta\sin\phi+\mathbf{\hat{k}}\cos\theta$, given that we know the matrix representations for $S_x, S_y, S_z$.
Apparently it suffices to write $S_n=\vec{S}\cdot\mathbf{\hat{n}}=S_x\sin\theta\cos\phi +S_y\sin\theta\sin\phi+ S_z\cos\theta$
What I don't get is: We are expressing $S_x, S_y, S_z$ as the components of the Spin vector, but those are matrices (operators). How is this right? I thought components of vectors could only be scalars.