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I have a code spitting out matrices $A$. I am trying to understand the structure of these matrices.

I have identified that we can always unitarily transform the matrix $A$ to $-A$ via a transform $A'=U^\dagger A U=-A$.

Is there any special name for this type of matrix?

And does this propery imply any others?

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  • $\begingroup$ It implies $\operatorname{tr}A=0$. On a vector space of odd dimension, it implies $\det A=0$. $\endgroup$ – J.G. Feb 23 at 14:42
  • $\begingroup$ It also implies that $tr(A)=0$ (more generally that for every eigenvalue $\lambda$ appearing with a Jordan block of length $n$ you get that $-\lambda$ appears with Jordan block of length $n$ as well). $\endgroup$ – Severin Schraven Feb 23 at 14:52

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