Question

I have to prove a linear transformation:
V is the set C of complex numbers regarded as a real vector space; Ax is the complex conjugate of x
But I am not sure about "Complex numbers regarded as a Real vector space"
Someone explains me, please

Answer 1

@mathmale

Answer 2

i think it just means that \(\mathbb{C}\) can be considered as vector space over the real numbers \(\mathbb{R}\) and any element of \(\mathbb C\) can be written as \(a+bi\) where \(a,b\in \mathbb R\)

Answer 3

i wouldn't worry to much about it, the proof is to show that the map \(T:\mathbb C\to \mathbb C\) via \[a+bi\mapsto a-bi\] is a linear map

Answer 4

or rather in your notation \(A(a+bi)=a-bi\)

Answer 5

Thank you so much @satellite73

Answer 6

yw