Sigma matrices question Group theory

[helpcometk]

Homework Statement

I have read the following text in a textbook(look the attaxhement) ,and i have a
simple question .WHY every 2x2 hermitian matrix would have to satisfy this Equation.It is not obvious to me why.Does anyone know the answer?
The textbook stops there without giving any answer.Is it something obvious?
Is there any lengthy calculation to show this?

Homework Equations

The Attempt at a Solution

 

[Dick]

Homework Statement

I have read the following text in a textbook(look the attaxhement) ,and i have a
simple question .WHY every 2x2 hermitian matrix would have to satisfy this Equation.It is not obvious to me why.Does anyone know the answer?
The textbook stops there without giving any answer.Is it something obvious?
Is there any lengthy calculation to show this?

Homework Equations

The Attempt at a Solution

It's sort of obvious just looking at the expression (5.27). Hermitian matrices have real diagonal elements and the two off-diagonal elements are complex conjugates. By selecting values of x0,x1,x2,x3 you can get any such matrix.

 

[helpcometk]

Yes its sort of obvious that I am stupid.
Thanks

 

[Dick]

Yes its sort of obvious that I am stupid.
Thanks

Hey, I miss the obvious too sometimes. Doesn't make you stupid.