Definition 18.4.1 (Adjoint Map).label Let $E, F$ be vector spaces over a field $K$, and $T \in \hom(E; F)$ be a linear map, then the mapping
\[T^{*}: F^{*} \to E^{*} \quad \dpn{x, T^*\phi}{E}= \dpn{Tx, \phi}{F}\]
is the algebraic adjoint of $T$.
Definition 18.4.1 (Adjoint Map).label Let $E, F$ be vector spaces over a field $K$, and $T \in \hom(E; F)$ be a linear map, then the mapping
is the algebraic adjoint of $T$.
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