On the normalizer of the reflexive cover of a unital algebra of linear transformationsBračič, Janko (Avtor) Kandić, Marko (Avtor) invariant subspacecollineationnormalizerreflexive coverGiven 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 $\mathrm{Col}(J_2 \oplus J_2)$.20222022-09-06 13:30:52Članek v reviji139720UDK: 517.983:512.643ISSN pri članku: 0024-3795DOI: 10.1016/j.laa.2022.08.013COBISS_ID: 119088643sl