Bra-ket notation

In quantum mechanics, ket is the name of the notation for the symbols | and > which enclose the label of a [quantum state]?. Thus |a> means: the quantum state we call a.

Kets represent column vectors in Hilbert space. They have counterparts called bras, which consist in the pair < and |, as in <a|, and which represent row vectors. To every ket there is a corresponding bra of the same dimensionality.

[Inner product]?s in the space are complex numbers that are written as <a|b>. [Outer product]?s are matrices that are written as |a><b|. An interesting use of the outer product is to denote the [projection operator]? on the [linear subspace]? spanned by, say, ket |a>. This is simply |a><a|.

Paul Dirac introduced this notation as a concise and convenient way to describe quantum states.