Week 5

Question 1

What is the definition of a eigenvalue?

Answer 1

lambda is an eigenvalue of A if there exists an non-zero vector v s.t. Av - lambda v.
v is call the eigenvector corresponding to lambda

Question 2

How to do the power method?

Answer 2

Take random vector x^(0), for k = 1, 2, …

z^(k + 1) = Ax^(k), r^(k) = (z.i^(k + 1))/(x.i^(k)), x^(k + 1) = z^(k + 1) / || z^(k + 1) ||

Question 3

What is the Inverse Power method?

Answer 3

Just the power method, but on the inverse

Question 4

How to do the shifted power method?

Answer 4

Just max | lambda.i - s |