# LA Ch8 Exs Prob P3 by 김지윤

## 508 days ago by jykim

x1=vector([3, 0, 0]);x2=vector([0,3, 4]); x3=vector([0, 4, 3]) A=column_matrix([x1, x2, x3]) print "eigenvalue of A=", A.eigenvalues() print print "eigenvector of A=" print A.right_eigenvectors() z1= A.right_eigenvectors()[0][1][0]/A.right_eigenvectors()[0][1][0].norm() z2= A.right_eigenvectors()[1][1][0]/A.right_eigenvectors()[1][1][0].norm() z3= A.right_eigenvectors()[2][1][0]/A.right_eigenvectors()[2][1][0].norm() P=column_matrix([z1,z2,z3]) Q=P.inverse() D=diagonal_matrix(A.eigenvalues()) print "P=" print P print print "D=" print D print print "A=" print P*D*Q
 eigenvalue of A= [7, 3, -1] eigenvector of A= [(7, [ (0, 1, 1) ], 1), (3, [ (1, 0, 0) ], 1), (-1, [ (0, 1, -1) ], 1)] P= [ 0 1 0] [ 1/2*sqrt(2) 0 1/2*sqrt(2)] [ 1/2*sqrt(2) 0 -1/2*sqrt(2)] D= [ 7 0 0] [ 0 3 0] [ 0 0 -1] A= [3 0 0] [0 3 4] [0 4 3] eigenvalue of A= [7, 3, -1] eigenvector of A= [(7, [ (0, 1, 1) ], 1), (3, [ (1, 0, 0) ], 1), (-1, [ (0, 1, -1) ], 1)] P= [ 0 1 0] [ 1/2*sqrt(2) 0 1/2*sqrt(2)] [ 1/2*sqrt(2) 0 -1/2*sqrt(2)] D= [ 7 0 0] [ 0 3 0] [ 0 0 -1] A= [3 0 0] [0 3 4] [0 4 3]