# Definition Given a [[vector space]] $V$ over a field $\mathbb{F}$, the dual space $V^*$ is the space of [[one-form|one-forms]] (i.e. dual vectors, [[Covector and Contravector|covectors]], or linear functionals). $V$ and $V^*$ always have the same [[dimension]]. They are [[Isomorphism|isomorphic]], but it is not a canonical isomorphism since we have to define the [[inner product]] first to get it. # In Physics The vector space of bras is dual to the [[Hilbert space]] of kets.