Constructing a Minimal Basis of Invariants for Differential Algebra of (Formula presented.) Matrices

Standard

Constructing a Minimal Basis of Invariants for Differential Algebra of (Formula presented.) Matrices. / Vasyutkin, S. A.; Chupakhin, A. P.

In: Journal of Applied and Industrial Mathematics, Vol. 16, No. 2, 05.2022, p. 356-364.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{cf2b9d89e7264a91ab7938f8e0e05e18,

title = "Constructing a Minimal Basis of Invariants for Differential Algebra of (Formula presented.) Matrices",

abstract = "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{\textquoteright}s formulas in terms of the traces of the product of matrices in this set.",

keywords = "affine invariant, algebraic invariants, differential invariant, Fricke formula, invariant differentiation operator, minimal basis of invariants",

author = "Vasyutkin, {S. A.} and Chupakhin, {A. P.}",

note = "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: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

month = may,

doi = "10.1134/S1990478922020156",

language = "English",

volume = "16",

pages = "356--364",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "2",

}

RIS

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