Finding eigenvector with existing eigenvalues

2 Ansichten (letzte 30 Tage)
Andreas Rüdisühli
Andreas Rüdisühli am 12 Jun. 2021
I have a really simple example, which I would like to use for a better understanding of Eigenvector calculation in Matlab:
A = [3 6; 4 8]
x1 = [0.75; 1]
x2 = [-2; 1]
λ1 = 11
λ2 = 0
Which code do I have to use to have the simple output of x1 & x2?
I've tried several codes I found but always got a strange output:
CODE 1:
A = [4 1; 3 2];
[V,D] = eig(A);
V1 = V(:,1)
V2 = V(:,2)
OUTPUT 1:
v1 = [0.7071; 0.7071]
v2 = [-0.3162; 0.9487]
CODE 2:
A = [4 1; 3 2];
lambda=eig(A); % you should do it by solving det(A-lambda I)=0
V = ones(2);
for k=1:2
B = A-lambda(k)*eye(size(A));
% select pivot column
[~,j] = max(sum(B.^2,1));
othercolumn = 3-j;
V(j,k) = -B(:,j)\B(:,othercolumn);
end
% Optional: Make eigenvectors l2 norm = 1
V = V ./ sqrt(sum(V.^2,1))
OUTPUT 2:
V = [0.7071 -0.3162; 0.7071 0.9487]
May someone help me to get the mentioned outputs x1 = [0.75; 1] & x2 = [-2; 1]?
Thanks!!
  2 Kommentare
SALAH ALRABEEI
SALAH ALRABEEI am 12 Jun. 2021
you system is not linear indpendent, this means that is infinit eigenvectors. So ur x1 and x2 eig values, are just a case.
Andreas Rüdisühli
Andreas Rüdisühli am 13 Jun. 2021
Oh I see, thanks!

Melden Sie sich an, um zu kommentieren.

Antworten (0)

Kategorien

Mehr zu Linear Algebra finden Sie in Help Center und File Exchange

Produkte


Version

R2020b

Community Treasure Hunt

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

Start Hunting!

Translated by