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Aug 5 at 1:39 vote accept user369335
Aug 14 at 7:09
Jun 13 at 12:32 answer added user369335 timeline score: 4
Jun 8 at 23:14 history edited user369335 CC BY-SA 4.0
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Jun 8 at 12:26 comment added Fedor Petrov Orthogonality means $A A^T=nI$ (where $I$ is identity matrix), if $A^T=A$, we get $A^2=nI$, thus eigenvalues of $A$ are only $\pm \sqrt{n}$. Therefore, if $n$ is not a perfect square, the sum of eigenvalues (i.e., trace) can be integer only if it is 0.
Jun 8 at 12:23 history edited user369335 CC BY-SA 4.0
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Jun 8 at 12:22 comment added user369335 The skew-symmetric definition here is slightly different than $A^T=-A$. @FedorPetrov
Jun 8 at 12:17 history edited user369335 CC BY-SA 4.0
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Jun 8 at 12:09 comment added Fedor Petrov How can it be skew-symmetric, should not skew-symmetric matrix have zeros on diagonal?
Jun 8 at 11:39 history asked user369335 CC BY-SA 4.0