Zobrazeno 1 - 10
of 188
pro vyhledávání: '"Guterman, Alexander"'
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
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
We investigate the class of finite dimensional not necessary associative algebras that have slowly growing length, that is, for any algebra in this class its length is less than or equal to its dimension. We show that this class is considerably big,
Externí odkaz:
http://arxiv.org/abs/2203.03641
We introduce and investigate the algebras of steadily growing length, that is the class of algebras, where the length is bounded by a linear function of the dimension. In particular we show that Malcev algebras belong to this class and establish the
Externí odkaz:
http://arxiv.org/abs/2203.03595
We study realizable values of the length function for unital possibly nonassociative algebras of a given dimension. To do this we apply the method of characteristic sequences and establish sufficient conditions of realisability for a given value of l
Externí odkaz:
http://arxiv.org/abs/2203.03593