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Eigenvector mystery
10-20-2020, 12:08 AM
Post: #11
RE: Eigenvector mystery
(10-19-2020 09:42 PM)Thomas Okken Wrote:  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.

Thomas is fully right.

You can find a program to compute the coefficients of the Characteristic Polynomial (its roots are the eigenvalues) for real or complex matrices in my article:

      HP Article VA047 - Boldly Going - Eigenvalues and Friends

Also, there are many solved examples in the article, to make the matter crystal-clear.

V.

  
All My Articles & other Materials here:  Valentin Albillo's HP Collection
 
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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 - 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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