*Problem 3.17 The 2 x 2 matrix representing a rotation of the xy-plane is cos 0 - sin 0 cos e T = sin 0 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 which diagonalizes T. Perform the similarity transformation (STS-) explicitly, and show that it reduces T to diagonal form.

*Problem 3.17 The 2 x 2 matrix representing a rotation of the xy-plane is cos 0 - sin 0 cos e T = sin 0 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 which diagonalizes T. Perform the similarity transformation (STS-) explicitly, and show that it reduces T to diagonal form.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 59P: At one point in space, the direction of the electric field vector Is given In the Cartesian system...

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