Also known as Dirac notation, the bra and ket notation highlights the difference between a wave function being thought of as a vector or a functional. So bra(φ‎) = ⟨φ‎| is a functional, in the dual space, acting on states ψ‎ by ⟨φ‎| : ψ‎↦⟨φ‎,ψ‎⟩, whereas ket(φ‎) = |φ‎⟩ represents a quantum state. Here ⟨,⟩ denotes the inner product.