the calculation of the eigenvector
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B =
1.0e+06 *
0.6064 -0.4550 0.0776 -0.6532 0.4550 0.0126
-0.4550 1.6724 0.0180 0.4550 -0.3209 0.0180
0.0776 0.0180 0.3626 -0.0126 -0.0180 0.0569
-0.6532 0.4550 -0.0126 1.0029 -0.4550 0.5070
0.4550 -0.3209 -0.0180 -0.4550 4.4121 -0.0180
0.0126 0.0180 0.0569 0.5070 -0.0180 0.9314
D1 =
a
b
c
d
e
f
how can i find the unkowns a b c d e f if [B]*[D1]==0 and [D1] is the eigenvector
please give me all the details and the coding because i'm new to MATLAB and i'm still learning it
And thank you in advanced.
2 Comments
John D'Errico
on 5 Oct 2020
Ameer - correct, in a sense. The matrix is full rank, and therefore no solution exists. The nullspace is theoretically empty. See my comment on Alan's answer.
Accepted Answer
Alan Stevens
on 5 Oct 2020
You seem a little confused about eigenvalues and eigenvectors. The following code might provide some clarification:
B = [0.6064 -0.4550 0.0776 -0.6532 0.4550 0.0126;
-0.4550 1.6724 0.0180 0.4550 -0.3209 0.0180;
0.0776 0.0180 0.3626 -0.0126 -0.0180 0.0569;
-0.6532 0.4550 -0.0126 1.0029 -0.4550 0.5070;
0.4550 -0.3209 -0.0180 -0.4550 4.4121 -0.0180;
0.0126 0.0180 0.0569 0.5070 -0.0180 0.9314]*10^6;
[V, D] = eig(B);
% The eigenvalues lie along the diagonal of D
% The corresponding eigenvectors are the columns of V
eigvals = diag(D);
disp('Eigenvalues')
disp(eigvals)
disp('Eigenvectors')
disp(V)
% Test Change n from 1 to 6 to check each one
n = 1;
LHS = B*V(:,n);
RHS = eigvals(n)*V(:,n);
disp('Check')
disp([LHS RHS])
This produces the following eigenvalues and eigenvectors
Eigenvalues
1.0e+06 *
0.0000
0.3368
0.6801
1.2532
2.0983
4.6193
Eigenvectors
-0.7069 0.1149 -0.5810 -0.0407 -0.3522 -0.1543
-0.0279 0.0922 -0.3828 -0.5569 0.7141 0.1551
0.0784 -0.9559 -0.2820 0.0225 -0.0076 0.0018
-0.6145 -0.1437 0.3404 0.4577 0.4967 0.1722
0.0092 -0.0249 0.0754 0.0193 0.2676 -0.9600
0.3400 0.2080 -0.5611 0.6912 0.2185 0.0286
6 Comments
Bruno Luong
on 5 Oct 2020
"so all i need to do is to take more than 4 decimal places in B to get more accurate results"
Not really, the lesson you should draw is that never post here a screen capture of matrix displaying alone. Give us your matrix in MAT format, unless you have a code to generate it.
You should avoid communicate numerical data with a screen output.
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