Self Adjoint and Skew Adjoint Linear Transformations

Question

I'm studying adjoints, and I'm confused as to how I prove this. I have a definition of a self-adjoint $T$, such that $T^*=T$, where $T^*$ is the adjoint. I then have that the definition of a skew-adjoint linear transformation is that $T^*=-T$. I then want to prove that any linear transformation can be written as the sum of a self-adjoint and a skew-adjoint transformation.

I really am stuck with where to begin on this question, any help really appreciated. Thanks.

Answer 1

Hint: If $T:V \to V$ is given, consider things like $T+T^*$ and $T-T^*$. (You will need the fact that $T^{**} = T$)