Section 5.2 The Characteristic Equation
Review: A x x
Find eigenvectors x by solving A
I x 0.
How do we find the eigenvalues ? x must be nonzero A I x 0 must have nontrivial solutions A I is not invertible det A I 0 (called the characteristic equation) So
Problem: What do we do when Ax b has no solution x?
Answer: Find x such that Ax is as close as possible to b. (Least
If A is m n and b is in R m , a least-squares solution of Ax b is
an x in R n suc