>[!quote] In a Nutshell >Also called Bra-Ket notation, alternative formalism for linear algebra and linear operators on complex [[Vector Space|vector spaces]] that is extensively used in quantum mechanics. --- A **ket** $|v \rangle$ denotes a vector $\mathbf{v}$ in an abstract (complex) [[Vector Space|vector space]] $V$ and represents the state of a system. A **bra** $\langle f|$ denotes a linear form $f \colon V \rightarrow \mathbb{C}$ that maps each vector in $V$ to a number. A linear functional acting on a vector is denoted $\langle f|v\rangle \in \mathbb{C}$.