# LA Ch8 Exs Prob 6 by 김지윤

## 1674 days ago by jykim

v1=vector([0, 0, 0, -1]);v2=vector([0,1, 0, 0]);v3=vector([0, 0, 1, 0]);v4=vector([-1, 0, 0, 0]) A=column_matrix([v1, v2, v3, v4]) print "A=" print A print print "eigenvalue of A" print A.eigenvalues() print print "eigenvector of A" print A.right_eigenvectors() z1= A.right_eigenvectors()/A.right_eigenvectors().norm() z2= A.right_eigenvectors()/A.right_eigenvectors().norm() z3= A.right_eigenvectors()/A.right_eigenvectors().norm() z4= A.right_eigenvectors()/A.right_eigenvectors().norm() P=column_matrix([z4,z3,z2,z1]) print print "P=" print P print print "D=" print P.transpose()*A*P
 A= [ 0 0 0 -1] [ 0 1 0 0] [ 0 0 1 0] [-1 0 0 0] eigenvalue of A [-1, 1, 1, 1] eigenvector of A [(-1, [ (1, 0, 0, 1) ], 1), (1, [ (1, 0, 0, -1), (0, 1, 0, 0), (0, 0, 1, 0) ], 3)] P= [ 1/2*sqrt(2) 1/2*sqrt(2) 0 0] [ 0 0 1 0] [ 0 0 0 1] [ 1/2*sqrt(2) -1/2*sqrt(2) 0 0] D= [-1 0 0 0] [ 0 1 0 0] [ 0 0 1 0] [ 0 0 0 1] A= [ 0 0 0 -1] [ 0 1 0 0] [ 0 0 1 0] [-1 0 0 0] eigenvalue of A [-1, 1, 1, 1] eigenvector of A [(-1, [ (1, 0, 0, 1) ], 1), (1, [ (1, 0, 0, -1), (0, 1, 0, 0), (0, 0, 1, 0) ], 3)] P= [ 1/2*sqrt(2) 1/2*sqrt(2) 0 0] [ 0 0 1 0] [ 0 0 0 1] [ 1/2*sqrt(2) -1/2*sqrt(2) 0 0] D= [-1 0 0 0] [ 0 1 0 0] [ 0 0 1 0] [ 0 0 0 1]