On algebraic-geometric properties of the sum of cyclic subspaces with respect to a linear operator

Title	On algebraic-geometric properties of the sum of cyclic subspaces with respect to a linear operator
Authors	V. I. Nikonov¹ ¹National Research Mordovia State University
Annotation	The algebraic and geometric properties of the sum of cyclic subspaces with respect to a linear operator, which arise in the study of linear control systems, are investigated. The resulting properties are expressed in terms of minimal annihilating polynomials of the sum and intersection of the corresponding cyclic subspaces. The canonical forms of the linear operator are considered both in partially consistent bases of subspaces and in the cyclic basis of the sum of these subspaces.
Keywords	linear operator, cyclic subspace, minimal annihilating polynomial.
Citation	Nikonov V. I. ''On algebraic-geometric properties of the sum of cyclic subspaces with respect to a linear operator'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 143-148. Available at: https://conf.svmo.ru/files/2024/papers/paper25.pdf. - Date of access: 16.10.2024.