200 II C11 0-12|C C 31 C 2 C13=3C13(row one) C13=0 C23+ 2C33=3C23(row two) 33=2C23(again the third row offers no new information) C132+C232+C332=1(from normalization) 5C232=1 C23=v0. 2, and therefore C33=2v0.2 Next, find the pair of eigenvectors associated with the degenerate eigenvalue of-2. First, root one eigenvector one 2C11=-2Cl1(no new information from row one) 1+2C31=-2C21( row two) C21=-2C31(again the third row offers no new information) 11+ C212+ C312=1(from normalization C1 C C11 5C312 Ith three unknowns. Second root two eigenvector two3 ë ê ê é û ú ú ù -2 0 0 0 -1 2 0 2 2 ë ê ê é û ú ú C ù 11 C21 C31 = 3 ë ê ê é û ú ú C ù 11 C21 C31 -2 C13 = 3C13 (row one) C13 = 0 -C23 + 2C33 = 3C23 (row two) 2C33 = 4C23 C33 = 2C23 (again the third row offers no new information) C132 + C232 + C332 = 1 (from normalization) 0 + C232 + (2C23) 2 = 1 5C232 = 1 C23 = 0.2 , and therefore C33 = 2 0.2 . Next, find the pair of eigenvectors associated with the degenerate eigenvalue of -2. First, root one eigenvector one: -2C11 = -2C11 (no new information from row one) -C21 + 2C31 = -2C21 (row two) C21 = -2C31 (again the third row offers no new information) C112 + C212 + C312 = 1 (from normalization) C112 + (-2C31) 2 + C312 = 1 C112 + 5C312 = 1 C11 = 1 - 5C312 (Note: There are now two equations with three unknowns.) Second, root two eigenvector two: