20.500.12556/RUL-139719 On the singular two-parameter eigenvalue problem II In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems, which is a key relation for many theoretical results and numerical methods for nonsingular multiparameter eigenvalue problems. In 2009, Muhič and Plestenjak extended the above relation to a class of singular two-parameter eigenvalue problems with coprime characteristic polynomials and such that all finite eigenvalues are algebraically simple. They introduced a way to solve a singular two-parameter eigenvalue problem by computing the common regular eigenvalues of the associated system of two singular generalized eigenvalue problems. Using new tools, in particular the stratification theory, we extend this connection to singular two-parameter eigenvalue problems with possibly multiple eigenvalues and such that characteristic polynomials can have a nontrivial common factor. singular two-parameter eigenvalue problem Kronecker canonical form minimal reducing subspace stratification singularni dvoparametrični problem lastnih vrednosti Kroneckerjeva kanonična oblika minimalni reducirajoči podprostor stratifikacija true false true Angleški jezik Slovenski jezik Članek v reviji 2022-09-06 13:17:28 2022-09-06 13:17:31 2022-09-16 04:11:44 0000-00-00 00:00:00 2022 0 0 Str. 433-451 Vol. 649 Sep. 2022 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.643:519.6 0024-3795 10.1016/j.laa.2022.05.013 111311363 1-s2.0-S0024379522002002-main.pdf 1-s2.0-S0024379522002002-main.pdf 1 ED3B1E105A802371AF6BEF01DCACC6E4 dacc807e8f0a6d8f254a0ba53ba1b2f5c22e99073114589075d1730724825bf9 d40b9a99-2dd5-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=160325 https://www.sciencedirect.com/science/article/pii/S0024379522002002 1 73776d53-2dd5-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=160324 Fakulteta za matematiko in fiziko 0 0 0