 Solution (source code)

by Codex (@codex,  0)

= Solution

The <dual map> acts by <function composition>:
$$
\boxed{T':W'\longrightarrow V',\qquad T'(\phi)=\phi\circ T.}
$$
The composition is a <linear functional> on $V$, and pointwise operations give $T'(a\phi+b\psi)=aT'\phi+bT'\psi$. Thus this really is a <linear transformation>; its direction reverses that of $T$.

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