Textbook: Mathematical Methods in the Physical Sciences

-1 7/2 -1/2 4. Let A = -2 9/2 -1/2 The vectors are all eigenvectors of A. -2 7/2 1/2 a) What are the eigenvalues? b) What is a matrix T that diagonalizes A; i.e., 7-AT is diagonal? (Since A is not sym- metric, T won't be orthogonal.) What is the resulting diagonal matrix? c) The vector v = + is also an eigenvector of A. What is the 1 eigenvalue of v? Find an eigenvector of A which is perpendicular to v