Let $T: V \rightarrow V$ linear transformation in finite dimension
why is it true that $(im(T^*))^{\perp}=KerT$
and what does even $im(T^*)$ means?
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Is $V$ finite dimensional? – G. Chiusole May 25 '20 at 16:44
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Yes, I will edit now – Sagigever May 25 '20 at 16:44
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1$T^* : V \rightarrow V$ is the adjoint operator to $T$ and $im(T^)$ is just the image of $T^$. See https://en.wikipedia.org/wiki/Hermitian_adjoint for the full definition and also a hint for the answer to your question. – Rick May 25 '20 at 16:45
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Also, $V$ is a vector space over $\mathbb R$ and not over $\mathbb C$, right? The answer changes depending over which of these fields is $V$ taken. – Rick May 25 '20 at 16:53
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they didn't given wich field is – Sagigever May 25 '20 at 16:54