Show that {A + A (transpose) } is hermatian and {A- A transpose) is Skew hermatian

Question

wasiqss · Answer

I HAVE no idea how to approach this

anonymous · Answer

do you know the proof that $\frac{f(x)+f(-x)}{2}$ is even and $\frac{f(x)-f(-x)}{2}$ is odd?  because if i remember correctly this is amost idential. you work from the definition of hermitian and skew

wasiqss · Answer

no im very bad at these stuff can you plz show the proof of my quesion

experimentx · Answer

G = (A + A')
G' = (A + A')' = A' + A ...

wasiqss · Answer

But @experiment what to write in t a prrof im asked to submit the full proof

anonymous · Answer

This only holds iff A is Hermatian. 

For a proof, just take the transpose and use the definition of Hermatian and skew Hermatian matrices.

anonymous · Answer

And @satellite73 I think the proof you are reminiscing  about is showing that every square matrix can be written as the sum of a symmetric and skew symmetric matrix.

anonymous · Answer

yes you are right, sorry

anonymous · Answer

oops, This works for any square matrix. My apologies!.

wasiqss · Answer

so ffm what is the right answer?

anonymous · Answer

The right answer is the proof that sat was  reminiscing also and should works here!

wasiqss · Answer

so i should write the proof of sattelite?

anonymous · Answer

Also the decomposition is unique.

anonymous · Answer

No, that was just a hint.

wasiqss · Answer

sorry bit confuses so what should i write ,whose solution?

anonymous · Answer

Sorry, I had to sleep at that time. Btw do you mean symmetric?

anonymous · Answer

otherwise the result doesn't hold.. or do you mean conjugate transpose?