Ok so i have two matrices in Physics
H = hw times a 3x3 matrix, diagonal elements 1,-1,-1 -- all other entries 0
B = b times a 3x3 matrix with first diagonal element a 1,1 = 1, a 2,3 = 1 and a 3,2 = 1 and all other entries 0 [a i,j means the entry is row i column j]
h,w,b are constants.
Ok so the 2 matrices are hermitian. and they commute. thus i should be able to find a basis of mutual eigenvectors..
H has eigen values hw, -hw (twice) and eigen vectors (1,0,0), (0,1,1), (0,1,0), (0,0,1)
B has eigenvalues -b,b (twice) and eigen vectors (0,1,-2), (1,0,0), (0,1,1), (1,1,1)
but that means the only common eigenvectors are (1,0,0) and (0,1,1). It seems something has gone wrong but i dont know what! Help please !
Find out how.