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Pairs of maps preserving singularity on subsets of matrix algebras
Linear Algebra and its Applications. 2022. Vol. 644. P. 1–27.
Let F be an algebraically closed field and Mn be the n × n matrix algebra over F. A total graph of the full matrix
algebra is the graph with Mn as vertices, and two distinct matrices A, B are adjacent if and only if A+B is singular. The
characterization of all the automorphisms of the total graph is an open question. Motivated by this problem, we study
pairs of maps on a subset of Mn preserving the singularity of matrix pencils A + λB. In particular, we characterize maps T1, T2 : Mn → Mn satisfying the condition A + λB is singular if and only if T1(A) + λT2(B) is singular, for any A, B ∈ Mn and any non-zero λ ∈ F. Namely, we prove that in this case T1 = T2 and they are of the form T1(A) = T2(A) = P AQ for all A ∈ Mn, or of the form T1(A) = T2(A) = P AtQ for all A ∈ Mn, where P, Q ∈ Mn are non-singular matrices.
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a
porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates
for flow characteristics which show the specific behavior of the fluid. Our estimates
are validated numerically. ...
Added: July 5, 2026
М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г.
Для руководителей и работников промышленности, научно-исследовательских и проектно-конструкторских институтов, высших учебных заведений, аспирантов и студентов, а также для специалистов, разрабатывающих, выпускающих и эксплуатирующих средства телекоммуникаций.
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Переход к глобальному информационному ...
Added: July 4, 2026
МФТИ, 2025.
абота редакции научного журнала «Труды Московского физико-технического института» (кратко «Труды МФТИ»), редакционной коллегии и редакционного совета осуществляется в соответствии с Положением, утвержденным ректором института. В состав редакционной коллегии входят руководители института, факультетов, институтских и факультетских кафедр. Главный редактор журнала —президент МФТИ, член-корр. РАН Кудрявцев Н.Н.
Журнал «Труды МФТИ» входит в базу данных РИНЦ (Российский Индекс Научного Цитирования) и доступен в электронной ...
Added: July 4, 2026
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2021 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
Added: June 27, 2026
Ivchenko A., Shestoperov A. I., Fomina E. V., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., Лукьянченко П. П., Computer Research and Modeling 2023 Vol. 15 No. 1 P. 129–140
In this article we propose a new approach to the analysis of econometric industry parameters for the industry consolidation level. The research is based on the simple industry automatic control model. The state of the industry is measured by quarterly obtained econometric parameters from each industry’s company provided by the tax control regulator. An approach ...
Added: June 26, 2026
Gusev I., Maksaev A., Promyslov V., Journal of Mathematical Sciences 2026 Vol. 299 No. 6
The regular graph of the space of n × m matrices over a field F is defined as the undirected graph whose vertices are matrices of rank min(n, m), and distinct matrices A and B are connected by an edge if and only if rk(A + B) < min(n, m). In this paper, for |F| ...
Added: May 25, 2026
Gusev I., Maksaev A., Promyslov V., Записки научных семинаров ПОМИ РАН 2025 Т. 542 С. 20–41
The regular graph of the space of n×m matrices over a field F is defined as an undirected graph whose vertices are matrices of rank min(n, m), and distinct matrices A and B are connected by an edge if and only if rk(A+B) < min(n, m). In this paper, for |F| > 4 and m, ...
Added: November 24, 2025
Sharma H., Shirokov D., Advances in Applied Clifford Algebras 2025 Vol. 35 Article 44
Commutative analogues of Clifford algebras are algebras defined in the same way as Clifford algebras except that their generators commute with each other, in contrast to Clifford algebras in which the generators anticommute. In this paper, we solve the problem of finding multiplicative inverses in commutative analogues of Clifford algebras by introducing a matrix representation ...
Added: October 2, 2025
Shirokov D., Advances in Applied Clifford Algebras 2025 Vol. 35 Article 25
We discuss a generalization of Clifford algebras known as generalized Clifford algebras (in particular, ternary Clifford algebras). In these objects, we have a fixed higher-degree form (in particular, a ternary form) instead of a quadratic form in ordinary Clifford algebras. We present a natural realization of unitary Lie groups, which are important in physics and ...
Added: May 20, 2025
Akhmedova E., Guterman A., Spiridonov I., Linear Algebra and its Applications 2025 Vol. 709 P. 331 – 341
Added: April 27, 2025
Shirokov D., , in: Advances in Computer Graphics: 41st Computer Graphics International Conference, CGI 2024, Geneva, Switzerland, July 1–5, 2024, Proceedings, Part IIIVol. 15340.: Springer, 2025. P. 336–348.
Added: April 1, 2025
Spiridonov I., Duffner M. A., Guterman A., Linear Algebra and its Applications 2021 Vol. 618 No. n/a P. 76–96
Added: October 3, 2024
Spiridonov I., Meshulam R., Гутерман А., Israel Journal of Mathematics 2023 Vol. 256 No. 1 P. 297 – 309
Added: October 3, 2024
Costara C., A. E. Guterman, A. M. Maksaev et al., Linear Algebra and its Applications 2023 Vol. 666 P. 129–143
In this paper, we characterize the automorphisms of the total graph for the ring M_n of matrices of order n≥2 over any field with at least 3 elements. To do this, we apply the technique of maps preserving matrix invariants; in particular, as an intermediate step, we characterize pairs of surjective maps φ_1,φ_2:M_n →M_n such that A+B is singular if and only if φ_1(A)+φ_2(B) is ...
Added: April 11, 2023
Shirokov D., Computational and Applied Mathematics 2021 Vol. 40 P. 1–29
In this paper, we solve the problem of computing the inverse in Clifford algebras of arbitrary dimension. We present basis-free formulas of different types (explicit and recursive) for the determinant, other characteristic polynomial coefficients, adjugate, and inverse in real Clifford algebras (or geometric algebras) over vector spaces of arbitrary dimension $n$. The formulas involve only ...
Added: July 15, 2021
Guterman A. E., Spiridonov I.A., Linear Algebra and its Applications 2020 Vol. 599 P. 140–155
Let $M_{n}(\mathbb{F})$ denote the set of square matrices of size $n$ over a field $\mathbb{F}$ with characteristics different from two. We say that the map $f: M_{n}(\mathbb{F}) \rightarrow M_{n}(\mathbb{F})$ is additive if $f(A+B) = f(A) + f(B)$ for all $A, B \in M_{n}(\mathbb{F})$. The main goal of this paper is to prove that for $n>2$ ...
Added: November 9, 2020
Shitov Y., Linear Algebra and its Applications 2018 Vol. 554 P. 49–50
We prove that the determinant of an n x n 01-matrix with at most n+k non-zero entries does not exceed α^k with α=4^(1/3)≈1.316074. ...
Added: January 30, 2019
Burman Y. M., Journal of Algebraic Combinatorics 2019 Vol. 50 No. 4 P. 427–446
The classical matrix-tree theorem discovered by G.Kirchhoff in 1847
expresses the principal minor of the (n x n) Laplace matrix as a
sum of monomials of matrix elements indexed by directed trees with n
vertices. We prove, for any k >= n, a three-parameter family of
identities between degree k polynomials of matrix elements of the
Laplace matrix. For k=n and special values of ...
Added: October 18, 2018
Shitov Y., Linear Algebra and its Applications 2018 Vol. 554 P. 49–50
We prove that the determinant of an n-by-n 0-1 matrix with at most n + k non-zero entries does not exceed α^k with α ≈ 1.316074. ...
Added: September 26, 2018