Then, the map
is bijective and satisfies:
this means that is an isomorphism and translates the structure of field from to .
Hi, I have the following two questions...I am not sure if I am in the right direction with the first one and I have no clue about the second one :-/
1.- Consider the set C of all matrices (with real entries) of the form
(sorry, I don't know how to code matrices! I'll separate each element with "|")
(a | -b)
(b | a)
The set C of matrices can clearly be identified with the complex numbers.
So I am a bit lost here... Why? Is it because, for example, if z=a+ib, its complex conjugate will be a-ib?
The next question is...
Continuing the previous exercise, how do the modulus and complex conjugate appear when translated into matrix terms? How does the reciprocal of the complex number z appears?
I would really appreciate it if you could give me a hint, thanks! I also tried to write the matrices using the code, but I go it wrong... I do not know if I am using an old version of the code or something