# Self Adjoint and Skew Adjoint Linear Transformations

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.

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