How to find number of linearly independent eigenvectors in a matrix?

15 visualizzazioni (ultimi 30 giorni)
I have a matrix
0 -1 -2 -1
-1 0 -1 0
-2 -1 0 -1
-1 0 -1 0
Each column represent an eigen vector, In the above case I have three linearly independent eigenvectors , How can I find this in matlab ?
  1 Commento
Ammy
Ammy il 10 Feb 2018
Also If I have 1000 of matrices how can I separate those on the basis of number of linearly independent eigenvectors, e.g I want to separate those matrices of order 4 by 4 having linearly independent eigen vectors 2.

Accedi per commentare.

Risposta accettata

possibility
possibility il 10 Feb 2018
In the context of Linear Algebra, one finds an eigenvalue of a matrix and then finds the right or the left eigenvector associated to that eigenvalue. Assume you have the matrix (your matrix)
A =
0 -1 -2 -1
-1 0 -1 0
-2 -1 0 -1
-1 0 -1 0
In order to have an idea of how many linearly independent columns (or rows) that matrix has, which is equivalent to finding the rank of the matrix, you find the eigenvalues first. And then you can talk about the eigenvectors of those eigenvalues.
Hence, if I understand it correctly, you're trying to find the rank of the matrix.
Following gives the number of linearly independent columns (or rows) of matrix A
>> rank(A)
ans =
3
And following outputs the eigenvalues (and their right eigenvectors) of that matrix
>> [eigenvec,eigenval]=eig(A)
eigenvec =
0.6015 -0.0000 0.3717 -0.7071
0.3717 0.7071 -0.6015 0.0000
0.6015 0.0000 0.3717 0.7071
0.3717 -0.7071 -0.6015 0.0000
eigenval =
-3.2361 0 0 0
0 0.0000 0 0
0 0 1.2361 0
0 0 0 2.0000
Hope that helps.

Più risposte (0)

Categorie

Scopri di più su Linear Algebra in Help Center e File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by