Finding eigenvector with existing eigenvalues

3 次查看（过去 30 天）

Andreas Rüdisühli 2021-6-12

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/854500-finding-eigenvector-with-existing-eigenvalues

评论： Andreas Rüdisühli 2021-6-13

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))