Show How to Write A as B + iC: Hermitian Operators

[Dragonfall]

How do I show that an arbitrary operator A can be writte as A = B + iC where B and C are hermitian?

 

[Edgardo]

Rewrite A as follows:

$$A = \frac{(A+A^{\dagger})}{2} + \frac{(A-A^{\dagger})}{2}$$

Do you see why you can write A like that?
And can you carry on?

 

[mathwonk]

anytime anywhere you have an involution J you can alwaYS WRiTE ANYTHIng AS

x = (x+JX)/2 + (X-JX)/2,

where X+JX is invariant under J, and X-JX is anti-invariant under J.

this is what lies beneath this fact.