It is worth reminding ourselves of one source of eigenvalue problems already considered in Chapter 1. As explained in Example 1.27, the following fact will guide many of our examples:


{cvˆ : c ∈ R}

~xi − projvˆ ~xi

(a) Input data (b) Principal axis (c) Projection error

When A is symmetric, the eigenvectors of A are the critical points of ~x>A~x under the constraint ‖~x‖2 = 1.