The MATLAB function eigshow is a graphical demonstration of eigenvalues and eigenvectors. When invoked by eigshow  where  is a  matrix, a graphical dialog appears. Do not press the button labeled...

The MATLAB function eigshow is a graphical demonstration of eigenvalues and eigenvectors. When invoked by eigshow where
 is a
 matrix, a graphical dialog appears. Do not press the button labeled eig/(svd). You will see two vectors, a unit vector
 and the vector
 We will show in Chapter 15 that as the tip of
 traces out the unit circle
²
₁

²
₂
 the tip of the vector
 traces out an ellipse whose center is the center of the circle. Move
 with the mouse until
 and
 are parallel, if you can. If you are successful,
 is a multiple of
 so
 Since x has length
 length
 and
 is an eigenvalue of
 corresponding to the eigenvector
 and its magnitude is Run eigshow for each of the following three matrices and estimate the eigenvalues, if you can make parallel to There are three possibilities: there are two distinct eigenvalues, a double eigenvalue, and two complex conjugate eigenvalues.