Eigenvector mystery
10-19-2020, 07:35 PM
Post: #8
 JurgenRo Member Posts: 176 Joined: Jul 2015
RE: Eigenvector mystery
(10-19-2020 07:19 PM)Thomas Okken Wrote:
(10-19-2020 07:13 PM)Albert Chan Wrote:  True, but so is M(kv) = w(kv)

For eigenvalue w, all kv are valid eigenvectors for it, as long as k ≠ 0

Also, eigenvalues with multiplicity greater than 1 correspond to subspaces with corresponding dimension, so in those cases the eigenvectors are not uniquely determined even if you normalize their lengths...

Uniqueness is not crucial. It's all about dimension of Eigenspaces (geometrical multiplicity) and to pick a finite set of linear independent vectors to form a base. That there are infinite vectors in a vectorspace is just part of the definition of a vectorspace (scalar multipication) and so it is irrelevant to mention it at all.
 « Next Oldest | Next Newest »

 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

User(s) browsing this thread: 1 Guest(s)