Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Digital systems, linear algebra and introduction to formal proof / 6 / c

Split $B$ into its symmetric part and skew-symmetric part: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.