This can be easily verified for $2\times2$ and $3\times3$ matrices, but can the result be generalised?
2026-03-26 23:09:56.1774566596
If a skew-symmetric real matrix has all eigenvalues zero, must it be the zero matrix?
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If the matrix has real entries: Any matrix with all eigenvalues zero is nilpotent, the only nilpotent skew-symmetric matrix is the zero matrix.