"let $ f $ be a homomorphism between two vector spaces $V$ and $W$, $f$ is endomorphism on $V$ if $im(f) \subseteq V$"
is correct? Thanks in advance!
2026-05-13 17:33:02.1778693582
About definition of endomorphism on vectos space
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This doesn't actually make sense unless we require $V$ to be a subspace of $W$. Normally we define an endomorphism to be a map from $V$ to $V$ with certain properties, specifically so that we don't have to worry about such technicalities.
But this definition is correct (assuming that by "homomorphism," you mean $\Bbb{F}$-linear map, where $\Bbb{F}$ is the underlying field) whenever $V$ is a subspace of $W$.