Amrozi, Rif`an (2020) Pembuktian Sifat non-Hausdorff dari Grup Lie GL(n,C) Bertindak pada M(n,C). Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Pada penelitian ini dibahas grup Lie General Linear GL(n,C) bertindak secara konjugasi pada manifold M(n,C). Himpunan semua orbit dari tindakan grup Lie tersebut dideskripsikan melalui bentuk kanonik Jordan yang merupakan ruangkuasi. Telah diduga jika X dan Y adalah matriks-matriksdi M(n,C) dengan nilai-nilai eigen yang sama tetapi memiliki bentuk kanonik Jordan yang berbeda, maka irisan dari persekitaran orbit dari Y dan persekitaran orbit dari X tidak kosong. Namun, pembuktian lengkap dari dugaan tersebut belum ada. Pada paper ini, diberikan pembuktian formal dugaan tersebut dengan perturbasi matriks, yaitu ruang kuasi yang berbentuk kanonik Jordan tersebut adalah suatu ruang non-Hausdorff.
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In this research, we discuss the action General Linear Lie Group GL (n, C) on manifold M (n, C) . The set of all orbits of this action is described through the Jordan canonical form which is a quasi-space. Already guessed if X and Y are matrices in M (n, C) with the same eigenvalues having different Jordan canonical form, then the intersection of the neighborhood of X and the neighborhood of Y is not empty set. However, complete proof of that hypothesis does not exist yet. In this final project, we provide proof that is thought to be related to the perturbation matrix, so that the quasi-space described through Jordan canonical form is a non-Hausdorff space.
| Item Type: | Thesis (Other) |
|---|---|
| Additional Information: | RSMa 519.537 Amr p-1 2020 |
| Uncontrolled Keywords: | Bentuk Kanonik Jordan, GL(n,C), Grup Lie, Hausdorff, Perturbasi Matriks |
| Subjects: | Q Science > QA Mathematics > QA159 Algebra Q Science > QA Mathematics > QA184 Algebra, Linear Q Science > QA Mathematics > QA9.58 Algorithms |
| Divisions: | Faculty of Mathematics, Computation, and Data Science > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Rif`an Amrozi |
| Date Deposited: | 17 Apr 2023 02:45 |
| Last Modified: | 17 Apr 2023 02:45 |
| URI: | http://repository.its.ac.id/id/eprint/74644 |
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