1. Eigenvalue problems and similarity / unitary transformation. Consider one of Pauli's 0-i (+) (a) Show that 02 is a Hermitian matrix. (0.5 point) (b) Show that 02 is an anti-symmetric

matrix. (0.5 point) (c) Solve an eigenvalue problem with 02, i.e., 02x = Ar. Find the eigenvalues and the unit- normalized eigenvectors of 02. There are two eigenvalues (A₁ and A2) and two eigenvectors (₁ and 2). Assume A₁ > A2. (1 point) matrices, 02 = for an eigenvalue problem. (d) Use the unit-normalized eigenvectors to find orthogonal matrix P which diagonalize 02 such that (1 point) (*). P-¹₂P.