eig and zero eigenvalues
14 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
I am working with a Laplacian matrix, L, and my understanding is that 0 will always be an eigenvalue of L with an algebraic multiplicity of at least 1. However, when I take
L = [2 -1 -1 0 0; 0 2 -1 -1 0; 0 0 2 -1 -1; -1 0 0 2 -1; -1 -1 0 0 2]
and compute eig(L), the result displays as
0.0000
2.5000 + 1.5388i
2.5000 - 1.5388i
2.5000 + 0.3633i
2.5000 - 0.3633i
but nnz(e) gives 5, and e > eps gives [1 1 1 1 1].
How do I get MATLAB to produce or recognize a truly 0 first/smallest eigenvalue? On my machine (MacBook Pro, OS X (10.6.8), MATLAB 7.12.0 (R2011a)), eps = 2.2204e-16 and that "zero" eigenvalue is actually 4.0392e-16.
I am interested in the algebraic multiplicity of the 0 eigenvalue and the smallest non-zero eigenvalue.
0 Kommentare
Akzeptierte Antwort
Titus Edelhofer
am 4 Jul. 2011
Hi,
your test is slightly wrong:
abs(e)>eps
ans =
0
1
1
1
1
Titus
5 Kommentare
Titus Edelhofer
am 4 Jul. 2011
Hi Matt,
what the "exact" factor would be, I don't know (L_inf norm of L, L_2 norm of L, something like that). Using norm(L, inf) should be a good value.
Titus
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Linear Algebra finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!