Calculating eigenvalue & eigenvectors manually

Hello everyone,

I am trying to write a program to find the eigenvalues and eigenvectors of a matrix manually ( without using eig() ).

This is my code here;

    [m,n]=size(A);
    y=zeros(0);
    syms lambda 
    %Eigenvalue calculation
    
    x=double(solve(det(A-lambda*eye(n)),lambda));
    eigenvalues=diag(x);
    uniqx=unique(x);
    [flag1,flag2]=size(x);
    [flag3,flag4]=size(uniqx);
    
    
            %Eigenvector calculation
                for i=1:flag3
                    B=null(A-uniqx(i)*eye(n));
                    B=B/norm(B);
                    y=[y B];
                end
        
       eigenvectors=y;

Unfourtunately I am stuck when I try to evaluate the eigenvectors of the corresponding "repeated" eigenvalues. Sometimes it returns me

every eigenvectors corresponds to that repeated value but sometimes it doesn't. I am trying to figure out the properties of the null statement in my code

as I think the problem occurs because of this but still I didn't get the point. (There might be mistakes in my code just critisize me if you see anything stupid :D)

Answer 1

[Esther mensah]

function [eigenvalues,eigenvectors] = eigen(mat)

syms x

I=eye(size(mat));

eigenvalues=double(solve(det(mat-x*I),x));

for i = 1:length(eigenvalues);

eigenvector= mat-(i)*I;

end