20.500.12556/RUL-139720 On the normalizer of the reflexive cover of a unital algebra of linear transformations Given a unital algebra ${\mathcal A}$ of linear transformations on a finite-dimensional complex vector space $V$, in this paper we study the set $\mathrm{Col}({\mathcal A})$ consisting of those invertible linear transformations $S$ on $V$ which map every subspace $M\in Lat({\mathcal A})$ to a subspace $SM\in \mathrm{Lat}({\mathcal A})$. We show that $Col({\mathcal A})$ is the normalizer of the group of invertible linear transformations in the reflexive cover of ${\mathcal A}$. For the unital algebra $(A)$ which is generated by a linear transformation $A$, we give the complete description of $\mathrm{Col}(A)$. By using the primary decomposition of $A$, we first reduce the problem of characterizing $\mathrm{Col}(A)$ to the problem of characterizing the group $\mathrm{Col}(N)$ of a given nilpotent linear transformation $N$. While $\mathrm{Col}(N)$ always contains all invertible linear transformations of the commutant of $(N)'$ of $N$, it is always contained in the reflexive cover of $(N)'$. We prove that $\mathrm{Col}(N)$ is a proper subgroup of $\mathrm{(AlgLat}(N)')^{-1}$ if and only if at least two Jordan blocks in the Jordan decomposition of $N$ are of dimension 2 or more. We also determine the group $\mathrm{Col}(J_2 \oplus J_2)$. invariant subspace collineation normalizer reflexive cover invarianten podprostor kolineacija normalizator refleksivno pokritje true false true Angleški jezik Slovenski jezik Članek v reviji 2022-09-06 13:30:52 2022-09-06 13:30:54 2022-09-22 12:07:18 0000-00-00 00:00:00 2022 0 0 Str. 207-230 Vol. 653 Nov. 2022 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.983:512.643 0024-3795 10.1016/j.laa.2022.08.013 119088643 1-s2.0-S0024379522002907-main.pdf 1-s2.0-S0024379522002907-main.pdf 1 23A122D589260F587D8ACAEE56C3CA0C b7cd4e050d1db72883751c9a8f7efc908bcf9ac63cff707e3322bf11bb0ece2c 8183ece6-2dd8-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=160329 https://www.sciencedirect.com/science/article/pii/S0024379522002907 1 519f6f3f-2dd7-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=160326 Naravoslovnotehniška fakulteta Fakulteta za matematiko in fiziko 0 0 0