Perturbation of invariant subspaces
Full text: english pdf 158 Kb
APA 6th Edition
Truhar, N. (1996). Perturbation of invariant subspaces. Mathematical Communications, 1 (1), 51-59. Retrieved from https://hrcak.srce.hr/1851
MLA 8th Edition
Truhar, N.. "Perturbation of invariant subspaces." Mathematical Communications, vol. 1, no. 1, 1996, pp. 51-59. https://hrcak.srce.hr/1851. Accessed 4 Jun. 2023.
Chicago 17th Edition
Truhar, N.. "Perturbation of invariant subspaces." Mathematical Communications 1, no. 1 (1996): 51-59. https://hrcak.srce.hr/1851
Truhar, N. (1996). 'Perturbation of invariant subspaces', Mathematical Communications, 1(1), pp. 51-59. Available at: https://hrcak.srce.hr/1851 (Accessed 04 June 2023)
Truhar N. Perturbation of invariant subspaces. Mathematical Communications [Internet]. 1996 [cited 2023 June 04];1(1):51-59. Available from: https://hrcak.srce.hr/1851
N. Truhar, "Perturbation of invariant subspaces", Mathematical Communications, vol.1, no. 1, pp. 51-59, 1996. [Online]. Available: https://hrcak.srce.hr/1851. [Accessed: 04 June 2023]
We consider two different theoretical approaches
for the problem of the perturbation of invariant subspaces.
The first approach belongs to the standard theory.
In that approach the bounds for the norm of the perturbation of the projector are proportional to the norm of perturbation matrix, and inversely proportional to the distance between the corresponding eigenvalues and the rest of the spectrum.
The second approach belongs to the relative theory which deals only with Hermitian matrices. The bounds which result from this approach are proportional to the size of relative perturbation of matrix elements
and the condition number of a scaled matrix, and inversely proportional to the relative gap between the corresponding eigenvalue and the rest of the spectrum. Because of a relative gap these bounds are in some cases less pessimistic than the standard norm estimates.
perturbation bound, invariant subspace, orthogonal projection
Visits: 1.688 *