Examinando por Autor "Danchev, Peter"

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Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence
(Elsevier, 2023) Danchev, Peter; García, Esther; Gómez Lozano, Miguel
For n ≥ 2 and fixed k ≥ 1, we study when an endomorphism f of Fn, where F is an arbitrary field, can be decomposed as t + m where t is a root of the unity endomorphism and m is a nilpotent endomorphism with mk = 0. For fields of prime characteristic, we show that this decomposition holds as soon as the characteristic polynomial of f is algebraic over its base field and the rank of f is at least n k , and we present several examples that show that the decomposition does not hold in general. Furthermore, we completely solve this decomposition problem for k = 2 and nilpotent endomorphisms over arbitrary fields (even over division rings). This somewhat continues our recent publications in Linear Multilinear Algebra (2022) and Int.
DECOMPOSITIONS OF MATRICES INTO A SUM OF INVERTIBLE MATRICES AND MATRICES OF FIXED NILPOTENCE
(International Linear Algebra Society, 2023-08-24) Danchev, Peter; García, Esther; Gómez Lozano, Miguel
For any $n\ge 2$ and fi xed $k\ge 1$, we give necessary and suficient conditions for an arbitrary nonzero square matrix in the matrix ring $\mathbb{M}_n(\mathbb{F})$ to be written as a sum of an invertible matrix $U$ and a nilpotent matrix $N$ with $N^k = 0$ over an arbitrary fi eld $\mathbb{F}$.
Decompositions of matrices into potent and square-zero matrices
(World Scientific Publishing, 2022-01-31) Danchev, Peter; García, Esther; Gómez Lozano, Miguel
On prescribed characteristic polynomials
(Elsevier, 2024-12) Danchev, Peter; García, Esther; Gómez Lozano, Miguel
Let F be a field. We show that given any nth degree monic polynomial q(x) ∈F[x] and any matrix A ∈Mn(F)whose trace coincides with the trace of q(x) and consisting in its main diagonal of k0-blocks of order one, with k