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.