Update 4_vector_spaces_QM.md

src/4_vector_spaces_QM.md

@@ -15,6 +15,9 @@ The lecture on vector spaces in quantum mechanics consists of four parts:
 
 ## Dirac notation and Hilbert spaces
 
+In the previous lecture we reviewed the basic properties of linear vector spaces. We know discuss how the same formalism
+can be applied to describe physical states in quantum mechanics.
+
 The state of a physical system in quantum mechanics is represented by a vector belonging to a complex vector space.
 This vector is known as the *state space* of the system.
 Such a physical state of a quantum system is represented by a symbol $|~~\rangle$, known  as a  *ket*.