# Complex Conjugation Vector Space

• February 9th 2009, 03:00 PM
krepka
Complex Conjugation Vector Space
Can someone help me with this vector proof?

Let V be the set of all complex-valued functions f on the real line such that (for all t in R)
f(-t)=f(t) bar (the bar denotes complex conjugation)
Show that V, with the operations
(f+g)(t) = f(t) + g(t)
(cf)(t) = cf(t)

is a vector space over the field of real numbers.
• February 9th 2009, 07:07 PM
ThePerfectHacker
Quote:

Originally Posted by krepka
Can someone help me with this vector proof?

Let V be the set of all complex-valued functions f on the real line such that (for all t in R)
f(-t)=f(t) bar (the bar denotes complex conjugation)
Show that V, with the operations
(f+g)(t) = f(t) + g(t)
(cf)(t) = cf(t)

is a vector space over the field of real numbers.

You basically need to show that if $f_1,f_2 \in V \implies f_1+f_2 \in V$ and $cf_1\in V$.