# LA.Ch8.Ex4.NEW.SC.Kim

## 2254 days ago by seongchan

A = matrix(5,5, [1,2,3,2,1,0,3,4,3,2,0,0,5,2,1,0,0,0,2,4,0,0,0,0,7]) print "A=",; print A print print "Eigenvalues of A" print A.eigenvalues() print print "Eigenvectors of A" print A.eigenvectors_right() print v1 = vector([1,144/113,78/113,48/113,60/113]) v2 = vector([1,8/7,4/7,0,0]) v3 = vector([1,1,0,0,0]) v4 = vector([1,1/2,1,-3/2,0]) v5 = vector([1,0,0,0,0]) P = column_matrix([v1, v2, v3, v4, v5]) print print P print print P^-1*A*P
 A= [1 2 3 2 1] [0 3 4 3 2] [0 0 5 2 1] [0 0 0 2 4] [0 0 0 0 7] Eigenvalues of A [7, 5, 3, 2, 1] Eigenvectors of A [(7, [ (1, 144/113, 78/113, 48/113, 60/113) ], 1), (5, [ (1, 8/7, 4/7, 0, 0) ], 1), (3, [ (1, 1, 0, 0, 0) ], 1), (2, [ (1, 1/2, 1, -3/2, 0) ], 1), (1, [ (1, 0, 0, 0, 0) ], 1)] [ 1 1 1 1 1] [144/113 8/7 1 1/2 0] [ 78/113 4/7 0 1 0] [ 48/113 0 0 -3/2 0] [ 60/113 0 0 0 0] [7 0 0 0 0] [0 5 0 0 0] [0 0 3 0 0] [0 0 0 2 0] [0 0 0 0 1] A= [1 2 3 2 1] [0 3 4 3 2] [0 0 5 2 1] [0 0 0 2 4] [0 0 0 0 7] Eigenvalues of A [7, 5, 3, 2, 1] Eigenvectors of A [(7, [ (1, 144/113, 78/113, 48/113, 60/113) ], 1), (5, [ (1, 8/7, 4/7, 0, 0) ], 1), (3, [ (1, 1, 0, 0, 0) ], 1), (2, [ (1, 1/2, 1, -3/2, 0) ], 1), (1, [ (1, 0, 0, 0, 0) ], 1)] [ 1 1 1 1 1] [144/113 8/7 1 1/2 0] [ 78/113 4/7 0 1 0] [ 48/113 0 0 -3/2 0] [ 60/113 0 0 0 0] [7 0 0 0 0] [0 5 0 0 0] [0 0 3 0 0] [0 0 0 2 0] [0 0 0 0 1]