RT Journal Article
T1 On prescribed characteristic polynomials.
A1 Danchev, Peter
A1 García González, Esther
A1 Gómez-Lozano, Miguel Ángel
K1 Polinomios
K1 Matrices (Matemáticas)
K1 Álgebra de tensores
K1 Álgebra lineal
AB 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 k 0-blocks of order one, with k < n − k, and an invertible non-derogatory block of order n − k, we can construct a square-zero matrix N such that the characteristic polynomial of A + N is exactly q(x). We also show that the restriction k < n − k is necessary in the sense that, when the equality k = n − k holds, not every characteristic polynomial having the same trace as A can be obtained by adding a square-zero matrix. Finally, we apply our main result to decompose matrices into the sum of a square-zero matrix and some other matrix which is either diagonalizable, invertible, potent or torsion.
PB Elsevier
YR 2024
FD 2024-08-13
LK https://hdl.handle.net/10630/32499
UL https://hdl.handle.net/10630/32499
LA eng
NO Peter Danchev, Esther García, Miguel Gómez Lozano, On prescribed characteristic polynomials, Linear Algebra and its Applications, Volume 702, 2024, Pages 1-18, ISSN 0024-3795, https://doi.org/10.1016/j.laa.2024.08.010
NO Institute of Mathematics and Informatics, Bulgarian Academy of SciencesUniversidad Rey Juan CarlosUniversidad de Malaga
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026