# [Final] Chapter 8 Problem 7 solved by 이나을 revised by 백지원 finalized by 강민혁+이나을

## 2395 days ago by math2013

A=matrix(QQ, 2,2, [-3,6,6,-3]) x1 = vector([-2, 2]) z1 = x1 / x1.norm() x2 = vector([5,5]) z2 = x2 / x2.norm() P = column_matrix([z1, z2]) print "Matrix P : " print P print print "Matrix D : " print P.transpose() * A * P
 Matrix P : [-1/2*sqrt(2) 1/2*sqrt(2)] [ 1/2*sqrt(2) 1/2*sqrt(2)] Matrix D : [-9 0] [ 0 3] Matrix P : [-1/2*sqrt(2) 1/2*sqrt(2)] [ 1/2*sqrt(2) 1/2*sqrt(2)] Matrix D : [-9 0] [ 0 3]
A=matrix(QQ,2,2,[-3,6,6,-3]) print A.eigenvalues() print A.eigenvectors_right()
 [3, -9] [(3, [ (1, 1) ], 1), (-9, [ (1, -1) ], 1)] [3, -9] [(3, [ (1, 1) ], 1), (-9, [ (1, -1) ], 1)]
A=matrix(QQ, 2,2, [7,2,2,4]) x1 = vector([2, 1]) z1 = x1 / x1.norm() x2 = vector([1,-2]) z2 = x2 / x2.norm() P = column_matrix([z1, z2]) print "Matrix P : " print P print print "Matrix D : " print P.transpose() * A * P
 Matrix P : [ 2/5*sqrt(5) 1/5*sqrt(5)] [ 1/5*sqrt(5) -2/5*sqrt(5)] Matrix D : [8 0] [0 3] Matrix P : [ 2/5*sqrt(5) 1/5*sqrt(5)] [ 1/5*sqrt(5) -2/5*sqrt(5)] Matrix D : [8 0] [0 3]
A=matrix(QQ,2,2,[7,2,2,4]) print A.eigenvalues() print A.eigenvectors_right()
 [8, 3] [(8, [ (1, 1/2) ], 1), (3, [ (1, -2) ], 1)] [8, 3] [(8, [ (1, 1/2) ], 1), (3, [ (1, -2) ], 1)]