Eigenvector mystery
10-19-2020, 07:19 PM
Post: #6
 Thomas Okken Senior Member Posts: 1,810 Joined: Feb 2014
RE: Eigenvector mystery
(10-19-2020 07:13 PM)Albert Chan Wrote:
(10-18-2020 10:54 PM)pinkman Wrote:  Eigenvalues (w) and eigenvectors (v) of a matrix (M) belong inseparably together and define each other: Mv=wv.

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...
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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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