I need to show that ever square matrix A can be expressed as the sum of a symmetric matrix and a skew symmetric matrix. I'm completely confused on this question... Should I answer this by filling in an actual matrix with variables, and then somehow come up with the appropriate symmetric matrices, or what?
Try starting with
So, we only have to prove that is
symmetric and that is skew symmteric.
Now, you do it for the other case, , and you're pretty much done.