The 2x2 matrix representing a rotation of the xy plane is

Show that (except for certain special angles—what are they?) this matrix has no real eigenvalues. (This reflects the geometrical fact that no vector in the plane is carried into itself under such a rotation; contrast rotations in three dimensions.) This matrix does, however, have complex eigenvalues and eigenvectors. Find them. Construct a matrix S that diagonalizes T. Perform the similarity transformation (STS^-1) explicitly, and show that it reduces T to diagonal form.

Transcribed Image Text:

T = COS A sin 6 - sin e 10). COS (A.91)