Zobrazeno 1 - 10
of 188
pro vyhledávání: '"Guterman Alexander"'
Publikováno v:
Special Matrices, Vol 9, Iss 1, Pp 112-118 (2021)
We combine matrix theory and graph theory methods to give a complete characterization of the surjective linear transformations of tropical matrices that preserve the cyclicity index. We show that there are non-surjective linear transformations that p
Externí odkaz:
https://doaj.org/article/4faac12c18c94cf8b8af6297d04df621
Publikováno v:
Special Matrices, Vol 8, Iss 1, Pp 40-60 (2020)
We study pairs of mutually orthogonal normal matrices with respect to tropical multiplication. Minimal orthogonal pairs are characterized. The diameter and girth of three graphs arising from the orthogonality equivalence relation are computed.
Externí odkaz:
https://doaj.org/article/a37030dc02cd4503b8df53c9fee56e5f
For an arbitrary normed space $\mathcal X$ over a field $\mathbb F \in \{ \mathbb R, \mathbb C \}$, we define the directed graph $\Gamma(\mathcal X)$ induced by Birkhoff-James orthogonality on the projective space $\mathbb P(\mathcal X)$, and also it
Externí odkaz:
http://arxiv.org/abs/2402.13416
Autor:
Guterman, Alexander, Zhilina, Svetlana
We compute the lengths of two particular cases of (possibly non-unital) composition algebras, namely, standard composition algebras and Okubo algebras over an arbitrary field $\mathbb{F}$. These results finish the complete description of lengths of s
Externí odkaz:
http://arxiv.org/abs/2312.03174
Autor:
Guterman, Alexander, Zhilina, Svetlana
We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field $\mathbb{F}$. We suggest a new method based on the sequence of differences between the dimensions of the linear spans of words, which allo
Externí odkaz:
http://arxiv.org/abs/2312.03170
Autor:
Guterman, Alexander, Spiridonov, Igor
Publikováno v:
Linear Algebra and its Applications, 680 (2024): 325-340
Let ${\rm Mat}_n(\mathbb{F})$ denote the set of square $n\times n$ matrices over a field $\mathbb{F}$ of characteristic different from two. The permanental rank ${\rm prk}\,(A)$ of a matrix $A \in{\rm Mat}_{n}(\mathbb{F})$ is the size of the maximal
Externí odkaz:
http://arxiv.org/abs/2308.14526
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable matrices, ho
Externí odkaz:
http://arxiv.org/abs/2303.13239
Publikováno v:
Israel Journal of Mathematics 256.1 (2023): 297-309
In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a bipa
Externí odkaz:
http://arxiv.org/abs/2212.11193
Publikováno v:
Special Matrices, Vol 2, Iss 1 (2014)
Letr Σn(C) denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C) -> Σn (C) satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +
Externí odkaz:
https://doaj.org/article/2ff4af3ebd7c4f9287b9f1498f27130d
We study the roots of polynomials over Cayley--Dickson algebras over an arbitrary field and of arbitrary dimension. For this purpose we generalize the concept of spherical roots from quaternion and octonion polynomials to this setting, and demonstrat
Externí odkaz:
http://arxiv.org/abs/2205.05605