Hi, everyone! While I was studying for my midterm, I encountered this question. ------ Consider the hermitian operator H that has the property that H4 = 1 What are the eigenvalues of the operator H? What are the eigenvalues if H is not restricted to being Hermitian? ------ What I am going to ask is that does it matter this operator have a different power like H6 or H5? I mean what is the role of the power in this question? Also, I couldn't figure out that how I can find the eigenvalues of such operator when it is not Hermitian? Thank you.