Question

Problem 2 Consider the matrix E = ( 0 a1 a2 0 ) with a1 and a2 real positive. a) Find the eigenvalues of E b) Find the eigenvectors of E c) Normalize the eigenvectors such that their norm is equal to 1 and write down the matrix ? that will allow you to transform E in its diagonal equivalent E'. d) In order for this transformation to be a rotation, ? needs to be orthogonal which means ?^T ? = I = ( 1 0 0 1 ). What is the condition on a1 and a2 for this to be true? e) In this case, rotate the matrix E and verify that E' is diagonal. f) If a1 = a2; what is the angle of the rotation?

          Problem 2

Consider the matrix E = ( 0  a1
                        a2  0 ) with a1 and a2 real positive.

a) Find the eigenvalues of E

b) Find the eigenvectors of E

c) Normalize the eigenvectors such that their norm is equal to 1 and write down the matrix ? that will allow you to transform E in its diagonal equivalent E'.

d) In order for this transformation to be a rotation, ? needs to be orthogonal which means ?^T ? = I = ( 1  0
                                                                                                                   0  1 ). What is the condition on a1 and a2 for this to be true?

e) In this case, rotate the matrix E and verify that E' is diagonal.

f) If a1 = a2; what is the angle of the rotation?

Problem 2

Consider the matrix E = ( 0 a1
a2 0 ) with a1 and a2 real positive.

a) Find the eigenvalues of E

b) Find the eigenvectors of E

c) Normalize the eigenvectors such that their norm is equal to 1 and write down the matrix ? that will allow you to transform E in its diagonal equivalent E'.

d) In order for this transformation to be a rotation, ? needs to be orthogonal which means ?^T ? = I = ( 1 0
0 1 ). What is the condition on a1 and a2 for this to be true?

e) In this case, rotate the matrix E and verify that E' is diagonal.

f) If a1 = a2; what is the angle of the rotation?

Added by Cynthia B.

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