Let $A \in \mathbb{R}^{N \times N}$ be a D4571: Real matrix.
Then
| (1) | \begin{equation} A = \frac{A + A^T}{2} + \frac{A - A^T}{2} \end{equation} |
| (2) | $\frac{A + A^T}{2}$ is a D399: Symmetric matrix |
| (3) | $\frac{A - A^T}{2}$ is an D5204: Antisymmetric matrix |