Quotient vector space

Given a vector space $𝐴$ over a field $𝕂$ and a vector subspace $𝐵 \leq 𝐴$ , the quotient space $𝐴 / 𝐵$ is just $𝐴$ with all the elements of $𝐵$ collapsed to zero, #m/def/linalg More formally, using the congruence relation

𝑥 \equiv 𝑦 ⟺ 𝑥 - 𝑦 \in 𝐵

we have $𝐴 / 𝐵 = 𝐴 / \equiv$ with $𝛼 [𝑎] + 𝛽 [𝑏] = [𝛼 𝑎 + 𝛽 𝑏]$ . Hence this is a special case of a quotient module.

#state/develop | #lang/en | #SemBr