[Final] Chapter 8 Problem 12 solved by 백지원 revised by 이나을 finalized by 강민혁+이나을 Final OK by SG Lee

2020 days ago by math2013

A=matrix(3,3,[5,2,0,2,6,2,0,2,7]) print "eigenvalues : " print A.eigenvalues() print print "eigenvectors : " print A.eigenvectors_right() print P = matrix(3,3,[1/3, 2/3, 2/3,2/3,1/3,-2/3,2/3,-2/3,1/3]) print "Matrix P : " print P print print "PT*A*P : " print P.transpose()*A*P 
       
eigenvalues : 
[9, 6, 3]

eigenvectors : 
[(9, [
(1, 2, 2)
], 1), (6, [
(1, 1/2, -1)
], 1), (3, [
(1, -1, 1/2)
], 1)]

Matrix P : 
[ 1/3  2/3  2/3]
[ 2/3  1/3 -2/3]
[ 2/3 -2/3  1/3]

PT*A*P : 
[9 0 0]
[0 6 0]
[0 0 3]
eigenvalues : 
[9, 6, 3]

eigenvectors : 
[(9, [
(1, 2, 2)
], 1), (6, [
(1, 1/2, -1)
], 1), (3, [
(1, -1, 1/2)
], 1)]

Matrix P : 
[ 1/3  2/3  2/3]
[ 2/3  1/3 -2/3]
[ 2/3 -2/3  1/3]

PT*A*P : 
[9 0 0]
[0 6 0]
[0 0 3]