The GATE Grind

GATE 2023 PH – Question 26

Mathematical Physics · matrices: similarity transformations, diagonalization, eigenvalues and eigen vectors · 1 mark · Multiple choice

A $4\times4$ matrix M satisfies $M^\dagger=-M$ and $M^4=\mathbf1$. Which is the correct eigenvalue set?

  1. $(1,1,-1,-1)$
  2. $(i,i,-i,-i)$
  3. $(i,i,i,-i)$
  4. $(1,1,-i,-i)$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) $(i,i,-i,-i)$

Explanation

Anti-Hermiticity makes eigenvalues imaginary; the fourth-power constraint restricts them to $\pm i$. B is an allowed spectrum.