Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Constructing a Minimal Basis of Invariants for Differential Algebra of (Formula presented.) Matrices. / Vasyutkin, S. A.; Chupakhin, A. P.
в: Journal of Applied and Industrial Mathematics, Том 16, № 2, 05.2022, стр. 356-364.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Constructing a Minimal Basis of Invariants for Differential Algebra of (Formula presented.) Matrices
AU - Vasyutkin, S. A.
AU - Chupakhin, A. P.
N1 - Funding Information: This work was supported financially by the Programs of Fundamental Scientific Research of the Siberian Branch of the Russian Academy of Sciences, project no. 2.3.1.2.10, code FWGG-2021-0009. Publisher Copyright: © 2022, Pleiades Publishing, Ltd.
PY - 2022/5
Y1 - 2022/5
N2 - We construct a basis of invariants for the set of second-order matrices consisting of theoriginal matrix and its derivatives. It is shown that the presence of derivatives imposes connectionson the elements of this set and reduces the number of elements in the basis compared to the purelyalgebraic case. Formulas for calculating algebraic invariants of such a set are proved. We state ageneralization of Fricke’s formulas in terms of the traces of the product of matrices in this set.
AB - We construct a basis of invariants for the set of second-order matrices consisting of theoriginal matrix and its derivatives. It is shown that the presence of derivatives imposes connectionson the elements of this set and reduces the number of elements in the basis compared to the purelyalgebraic case. Formulas for calculating algebraic invariants of such a set are proved. We state ageneralization of Fricke’s formulas in terms of the traces of the product of matrices in this set.
KW - affine invariant
KW - algebraic invariants
KW - differential invariant
KW - Fricke formula
KW - invariant differentiation operator
KW - minimal basis of invariants
UR - http://www.scopus.com/inward/record.url?scp=85142209191&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/7680f10d-fc09-323a-81b3-c45710f03efb/
U2 - 10.1134/S1990478922020156
DO - 10.1134/S1990478922020156
M3 - Article
AN - SCOPUS:85142209191
VL - 16
SP - 356
EP - 364
JO - Journal of Applied and Industrial Mathematics
JF - Journal of Applied and Industrial Mathematics
SN - 1990-4789
IS - 2
ER -
ID: 39709390