Eigenvector mystery
10-21-2020, 06:58 PM (This post was last modified: 10-21-2020 07:04 PM by JurgenRo.)
Post: #14
 JurgenRo Member Posts: 176 Joined: Jul 2015
RE: Eigenvector mystery
(10-21-2020 06:57 PM)JurgenRo Wrote:
(10-20-2020 12:08 AM)Valentin Albillo Wrote:  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.
Well, a few things should still be mentioned here (post by Thomas):
1. for the characteristic polynomial p(x)=|A-xI|, the term |A-xI| denotes the determinant of (A-xI).
2. the algebraic multiplicity of an eigenvalue (i.e. the multiplicity as zero of p) is always >= geometric multiplicity (i.e. the dimension of the eigenspace belonging to the eigenvalue).
3. I am not sure if "Dimension of a Matrix" is a valid definition. It's simply the number of rows (or columns).