I was wondering why quotient space is so important? Let say for vector space why quotient space is needed? Please explain!
2026-04-06 18:05:47.1775498747
Why quotient space is needed?
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It is important for vector spaces because of the theorem that for every surjective linear map $f : V \to W$ the map $f$ induces an isomorphism between the quotient space $V / \text{Kernel}(f)$ and $W$. There are similar theorems in other categories.