Dirac Notation:

The standard notation for a state vector is a ket vector |$\Psi$$\rangle$. For example, a vector in $\Real^{{3}}_{}$ with basis $\hat{{i}}$,$\hat{{j}}$,$\hat{{k}}$ is typically written as

$$\vec{{v}}$$ = a$$\hat{{i}}$$ + b$$\hat{{j}}$$ + c$$\hat{{k}}$$ = (a, b, c)^T.

In Dirac notation, it would be written as

| v$$\rangle$$ = a| i$$\rangle$$ + b| j$$\rangle$$ + c| k$$\rangle$$ = (a, b, c)^T.

The term ket and this notation come from the physicist Paul Dirac who wanted a concise way of writing formulas involving row and column vectors. He referred to row vectors as bra vectors represented as $\langle$y|. The inner product of a bra and a ket vector is written $\langle$y| x$\rangle$, and is called a bracket [18].