Eigenvector mystery

[Thomas Okken]

(10-19-2020 08:57 PM)pinkman Wrote:  

(10-19-2020 06:33 PM)JurgenRo Wrote:  You should really reread this in a textbook

Now I did!
What is still obscure for me is how the choice of eigenvalues are made by the algorithm.

Eigenvalues are values λ such that Av = λv, so you find them by solving Av − λv = 0, or equivalently, (A − λI)v = 0, where I is the identity matrix, or equivalently, |A − λI| = 0. That last form is also known as the characteristic equation of A, and, being a polynomial of the same degree as the dimension of A, you can find its solutions, and thus the eigenvalues of A, using a polynomial root finder.