Dual module

Let $𝑉$ be a left $𝑅$ -module. The dual module $𝑉 *$ is the space of all linear functions $𝑉 \to 𝑅$ , i.e. as a set $𝑉 * = 𝑅 𝖬 𝗈 𝖽 (𝑉, 𝑅)$ . #m/def/module The additional and scalar multiplication are pointwise. Sometimes we denote evaluation by

⟨ 𝑓, 𝑣 ⟩ = 𝑓 (𝑣)

for $𝑓 \in 𝑉 *$ , $𝑣 \in 𝑉$ .

#state/tidy | #lang/en | #SemBr