What is an example of a map $T$ from a complex vector space $C$ to itself such that $T(v+w)=T(v)+T(w)$. but $T$ is not linear.
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4Complex conjugation. – lulu Nov 20 '19 at 18:47
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2Complex conjugation? You'd have $\overline{v+w}=\overline{v}+\overline{w}$ but $\overline{iv}\neq i\overline{v}$ – JMoravitz Nov 20 '19 at 18:47
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1What about $T(x+yi)=x, $ for $x,y\in\mathbb R$? – J. W. Tanner Nov 20 '19 at 18:49
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What if the vector space is $C^n$ instead? – user 6663629 Nov 20 '19 at 18:51
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1@user42493 then take map which is additive on each coordinate, – robin3210 Nov 20 '19 at 19:03