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

S. A. Vasyutkin; A. P. Chupakhin

doi:10.1134/S1990478922020156

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

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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’s formulas in terms of the traces of the product of matrices in this set.

Original language	English
Pages (from-to)	356-364
Number of pages	9
Journal	Journal of Applied and Industrial Mathematics
Volume	16
Issue number	2
DOIs	https://doi.org/10.1134/S1990478922020156
Publication status	Published - May 2022

Keywords

affine invariant
algebraic invariants
differential invariant
Fricke formula
invariant differentiation operator
minimal basis of invariants

OECD FOS+WOS

1.01 MATHEMATICS
2.03 MECHANICAL ENGINEERING

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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.",

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

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AU - Chupakhin, A. P.

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KW - algebraic invariants

KW - differential invariant

KW - Fricke formula

KW - invariant differentiation operator

KW - minimal basis of invariants

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

Abstract

Keywords

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