Eigenvector mystery
10-19-2020, 09:42 PM
Post: #10
 Thomas Okken Senior Member Posts: 1,810 Joined: Feb 2014
RE: Eigenvector mystery
(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.
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 Messages In This Thread Eigenvector mystery - John Keith - 10-18-2020, 09:31 PM RE: Eigenvector mystery - pinkman - 10-18-2020, 10:54 PM RE: Eigenvector mystery - JurgenRo - 10-19-2020, 06:33 PM RE: Eigenvector mystery - Albert Chan - 10-19-2020, 07:13 PM RE: Eigenvector mystery - Thomas Okken - 10-19-2020, 07:19 PM RE: Eigenvector mystery - JurgenRo - 10-19-2020, 07:35 PM RE: Eigenvector mystery - JurgenRo - 10-19-2020, 07:26 PM RE: Eigenvector mystery - pinkman - 10-19-2020, 08:57 PM RE: Eigenvector mystery - Thomas Okken - 10-19-2020 09:42 PM RE: Eigenvector mystery - Valentin Albillo - 10-20-2020, 12:08 AM RE: Eigenvector mystery - JurgenRo - 10-21-2020, 06:57 PM RE: Eigenvector mystery - JurgenRo - 10-21-2020, 06:58 PM RE: Eigenvector mystery - Albert Chan - 10-18-2020, 11:58 PM RE: Eigenvector mystery - Michael de Estrada - 10-20-2020, 11:16 PM RE: Eigenvector mystery - John Keith - 10-24-2020, 02:03 PM RE: Eigenvector mystery - Albert Chan - 10-26-2020, 04:25 PM RE: Eigenvector mystery - John Keith - 10-27-2020, 12:37 PM

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