# Prove that an Eigen value of anti-symmetric matrix is either zero or

How to prove the following:

1. Prove that an eigenvalue of anti-symmetric matrix is either zero or imaginary.
2. Prove that the eigenvectors of a symmetric tensor are orthogonal.
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As $A^T=-A$, we conclude $(iA)^*=iA$. –  Hagen von Eitzen Jan 31 '13 at 13:03
Since $A^T = -A$, $(iA)^* = iA$; that is, $iA$ is self-adjoint, hence has real eigenvalues; it follows that $A$ has imaginary eigenvalues.