Inner Product Representations of Linear Functionals
Result
Suppose $V$ is a finite-dimensional vector space
and $\phi $ is a linear functional on $V$.
Then there exists a unique vector $u \in V$
satisfying
\[ \phi (b) = \ip{v, u} \quad \text{for all } v \in V \]
The above result is sometimes called the Riesz Representation Theorm.