A ket left bracketing bar ψ〉 is a vector living in a dual vector space to that containing bras 〈ψ right bracketing bar . Bras and kets are commonly encountered in quantum mechanics. Bras and kets can be considered as 1-vectors and 1-forms (or vice versa), although this is almost always done only in a finite-dimensional vector space. Considered as an inner product, the bra and ket form an angle bracket (bra+ket = bracket) 〈ψ|ψ〉.

angle bracket | bra | contravariant vector | covariant vector | differential k-form | inner product | L^2-inner product | one-form