What is meant by $\text{coordinatewise complex conjugation}$ in group action?

Question

$\text{Group Action}:$

What is meant by $\text{coordinatewise complex conjugation}$ in group action ?

Do there there exists any concept of $\text{conjugation}$ in Group action ?

I am week in Group action theory.

This context is from my previous question on Group action here what is the action of $\operatorname{Aut}(\mathbb{Z})$ on $\mathbb{C}^n$, see the comment of @Arturo Magidin

Can someone explain it shortly with an example?

You might want to give us the context where you encountered this statement. — Severin Schraven, Jul 18 '19 at 10:13

score 3 · Accepted Answer · answered Jul 18 '19 at 10:17

Judging without context, I presume your have some vector $(c_1, c_2, \dots, c_n) \in \mathbb C^n$. In this case, the componentwise complex conjugation will be $(c_1^*, c_2^*, \cdots, c_n^*) \in \mathbb C^n$, since you are conjugating the complex vector componentwise.

What is meant by $\text{coordinatewise complex conjugation}$ in group action?

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