Solution
= Solution
Split $B$ into its <symmetric part> and <skew-symmetric part>:
$$
\boxed{B=\underbrace{\frac{B+B^\top}{2}}_{S}+\underbrace{\frac{B-B^\top}{2}}_{K}.}
$$
Taking the <transpose> gives $S^\top=S$ and $K^\top=-K$. Thus $S$ is a <symmetric matrix> and $K$ a <skew-symmetric matrix>. These formulas also show uniqueness, since a real <matrix> that is both symmetric and skew-symmetric is zero.