I'm learning about that. I'd like to know the proof if is that true or if is not any example that make it fail. I'd also like to know about any good book with related information, i've read Grossman and Pita Ruiz linear Algebra, but i'd like to know more about it. Thanks.
2026-03-25 11:32:33.1774438353
Is an endomorphism always an isomorphism?
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An endomorphism of a vector space $V$ is a linear map $L : V \to V$. An automorphism of a vector space $V$ is an invertible linear map $L : V \to V$ (i.e. an automorphism is an invertible endomorphism). So every automorphism is an endomorphism, but the converse is not true. For example, if $\dim V > 0$, the map $L : V \to V$, $v \mapsto 0$ is an endomorphism, but it is not an isomorphism as it is not invertible (it has non-trivial kernel).