Skew-Symmetric Matrices#
Theorem: Skew-Symmetry via Negative Transpose
A square matrix \(M \in F^{}\) is skew-symmetric if and only if it is equal to the negative of its transpose:
\[M = -M^{\mathsf{T}}\]
Proof
TODO
Theorem: Skew-Symmetry \(\implies\) Zero Diagonal
If a square matrix is skew-symmetric, then the elements on its diagonal are all zeros.
Proof
TODO