I have matrix A, calculate null(A) but then A*null(A) doesn't give me 0?
6 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
%a) The traffic flow is an overdetermined system 12 variables to 9 equations
A = [-1 0 0 0 0 0 0 1 0 0 0 0;
1 1 0 0 0 0 0 0 0 0 -1 0;
0 -1 1 0 0 0 0 0 0 0 0 0;
0 0 -1 -1 0 0 0 0 0 0 0 1;
0 0 0 1 1 0 0 0 0 0 0 0 ;
0 0 0 0 1 1 0 0 -1 0 0 0;
0 0 0 0 0 -1 1 0 0 0 0 0;
0 0 0 0 0 0 -1 -1 0 1 0 0;
0 0 0 0 0 0 0 0 1 -1 1 -1];
b = [0; 150; 20; -410; 180; 210; 80; -230; 0];
%b)Gives five free variables, so there is not a unique solution,
%meaning the traffic flow depends in other intersects
x = linsolve(A,b);
%e)
nullspace = null(A) %Three vectors in the nullspace
nullVector = A* nullspace(:,1) %Shouldn't this give me zero vector?
I am wondering if I calculate null(A) and tree null vectors:
0.0939 0.3560 -0.3875
-0.1103 0.2839 0.4184
-0.1103 0.2839 0.4184
-0.0000 0.0000 0.0000
0.0000 -0.0000 -0.0000
0.4610 -0.0825 0.2202
0.4610 -0.0825 0.2202
0.0939 0.3560 -0.3875
0.4610 -0.0825 0.2202
0.5549 0.2734 -0.1674
-0.0164 0.6399 0.0309
-0.1103 0.2839 0.4184
Shouldn't that mean A*nullspaceVector = 0 ?
But nullVector = A* nullspace(:,1) gives me:
nullVector =
1.0e-15 *
0.0139
-0.1180
0.3053
-0.3053
-0.0714
0.2776
-0.1665
0.2220
0.0971
1 commentaire
Bruno Luong
le 21 Oct 2020
Modifié(e) : Bruno Luong
le 21 Oct 2020
1.0e-15 * somenumber is considered as 0 numerically in floating point calculation.
Illustration of the same thing with simpler example
>> x=[3 4];
>> y=null(x)
y =
-0.8000
0.6000
>> x*y
ans =
-4.4409e-16
Réponses (1)
Steven Lord
le 21 Oct 2020
Note that the description of the output argument on the documentation page for the null function does not include the character 0. It says that Z satisfies two properties, the key one of which for this question is "A*Z has negligible elements."
I would call 1e-15 or 1e-16 negligible relative to the elements in your matrix.
0 commentaires
Voir également
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!