How can I proof the following statement?
Any $n \times n$ matrix $A$ can be written as a sum $$ A = B + C $$ where $B$ is symmetric and $C$ is skew-symmetric.
I tried to work out the properties of a matrix to be symmetric or skew-symmetric, but I could not prove this. Does someone know a way to prove it?
PS: The question Prove: Square Matrix Can Be Written As A Sum Of A Symmetric And Skew-Symmetric Matrices may be similiar, in fact gives a hint to a solution, but if someone does not mind in expose another way, our a track to reach to what is mentioned in the question of the aforementioned link.