An issue with eigenvectors...

Question

Santiago Piñon 2022-11-27

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1864393-an-issue-with-eigenvectors

评论： Santiago Piñon 2022-11-27

When i execute this it only shows the last vector, not the first or second one.

clc

clear variables;

prompt = ("Ingrese su matriz de coeficientes ");

w=input(prompt);

fprintf("La matriz ingresada es\n");

disp(w)

sz=size(w);

tm=sz(1,1);

p=round(poly(w));

e = eig(w);

fprintf('**Los valores propios del sistema son: \n');

disp(e);

v1=e(1,1);

v2=e(2,1);

v3=e(3,1);

tf=isreal(e);

if(tf==1)

fprintf('**Los vectores propios del sistema son: \n');

L1=null(w-(v1*eye(tm)), 'r');

disp(L1);

L2=null(w-(v2*eye(tm)), 'r');

disp(L2);

L3=null(w-(v3*eye(tm)), 'r');

disp(L3);

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Answer 1

Bruno Luong 2022-11-27

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1864393-an-issue-with-eigenvectors#answer_1113083

在 MATLAB Online 中打开

Remove the rational option "r" (not reliable) you'll be fine

w = magic(3)
w = 3×3
     8     1     6
     3     5     7
     4     9     2
disp(w)
     8     1     6
     3     5     7
     4     9     2
sz=size(w);
tm=sz(1,1);
p=round(poly(w));
e = eig(w); 
fprintf('**Los valores propios del sistema son: \n');
**Los valores propios del sistema son: 
disp(e);
   15.0000
    4.8990
   -4.8990
v1=e(1,1);
v2=e(2,1);
v3=e(3,1);
tf=isreal(e);
if(tf==1)
    fprintf('**Los vectores propios del sistema son: \n');
    L1=null(w-(v1*eye(tm)));
    disp(L1);
    L2=null(w-(v2*eye(tm)));
    disp(L2);
     L3=null(w-(v3*eye(tm)));
     disp(L3);
end
**Los vectores propios del sistema son: 
    0.5774
    0.5774
    0.5774
   -0.8131
    0.4714
    0.3416
   -0.3416
   -0.4714
    0.8131

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Bruno Luong 2022-11-27

编辑：Bruno Luong 2022-11-27

No "r" is NOT correct in general, as stated by the offiial doc page

Z = null(A,"rational") returns a rational basis for the null space of A that is typically not orthonormal. If A is a small matrix with small integer elements, then the elements of Z are ratios of small integers. This method is numerically less accurate than null(A).

It is just a toy option forr students who works with academic examples. That's why it fails to return the eigen vector randomly.

Santiago Piñon 2022-11-27