The Characteristic Polynomial: When the Box Collapses
An interactive live film: the box of A - lambda I goes flat exactly at the roots of p(lambda) = det(A - lambda I), the eigenvalues; their sum is the trace and their product the determinant. Find the largest eigenvalue.
Narration
Take a three by three matrix A, and subtract lambda times the identity. The three columns of A minus lambda I span a box.
Changing lambda slides every column along its own coordinate axis, so the box stretches, shears and turns.
The rest of the narration is in the book's Companion.
