In one of tasks I met the concept of unitarily similar matrices: in particular, I need to prove that sets $\gamma_{\mu}, -\gamma_{\mu}$ (Dirac gamma matrices) are unitarily similar. I don't know what does it mean, so can someone tell me? Maybe, I need to find some unitary transformation that connects first and second sets?


1 Answer 1


I) Two square matrices $A$ and $B$ are similar matrices if they are connected via a relation $$\tag{1}AP~=~PB$$ for some invertible matrix $P$.

II) Two square matrices $A$ and $B$ are unitarily similar matrices if $P$ in eq. (1) is a unitary matrix.

  • $\begingroup$ Thank you! So in my case $\hat {U}^{+}\gamma_{\mu}\hat {U} = -\gamma_{\mu}$? $\endgroup$ Commented Feb 19, 2014 at 18:27
  • $\begingroup$ @Andrew McAddams: Yes. $\endgroup$
    – Qmechanic
    Commented Feb 19, 2014 at 18:34

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