^^ [[Schutz - 2 - Differentiable Manifolds and Tensors|2. Differentiable Manifolds and Tensors]] << [[Schutz - 2.16 - One-Forms|2.16 One-Forms]]|[[Schutz - 2.19 - The Gradient and the Pictorial Representation of a One-Form|2.19 The Gradient and the Pictorial Representation of a One-Form]]>> # Examples of One-Forms The most common example of vectors is column vectors in matrix algebra, and then row vectors become one-forms since they map vectors into numbers. Another example is the Hilbert spaces used in Quantum Mechanics, where the bra $\langle \phi|$ is the one-form and the ket $\psi\rangle$ is the vector, and they map each other into numbers $\langle \phi | \psi \rangle$