Zobrazeno 1 - 10
of 373
pro vyhledávání: '"A. Boussairi"'
A real matrix $Q$ is quasi-orthogonal if $Q^{\top}Q=qI$, for some positive real number $q$. We prove that any $n\times n$ skew-symmetric matrix $S$ is a principal sub-matrix of a skew-symmetric quasi-orthogonal matrix $Q$, called a quasi-orthogonal e
Externí odkaz:
http://arxiv.org/abs/2410.19594
A tournament is $k$-spectrally monomorphic if all the $k\times k$ principal submatrices of its adjacency matrix have the same characteristic polynomial. Transitive $n$-tournaments are trivially $k$-spectrally monomorphic. We show that there are no ot
Externí odkaz:
http://arxiv.org/abs/2112.05460
A tournament is unimodular if the determinant of its skew-adjacency matrix is $1$. In this paper, we give some properties and constructions of unimodular tournaments. A unimodular tournament $T$ with skew-adjacency matrix $S$ is invertible if $S^{-1}
Externí odkaz:
http://arxiv.org/abs/2109.11809
Publikováno v:
In Linear Algebra and Its Applications 15 August 2024 695:28-48
A generalized tournament matrix $M$ is a nonnegative matrix that satisfies $M+M^{t}=J-I$, where $J$ is the all ones matrix and $I$ is the identity matrix. In this paper, a characterization of generalized tournament matrices with the same principal mi
Externí odkaz:
http://arxiv.org/abs/2105.02715
Given a 3-hypergraph $H$, a subset $M$ of $V(H)$ is a module of $H$ if for each $e\in E(H)$ such that $e\cap M\neq\emptyset$ and $e\setminus M\neq\emptyset$, there exists $m\in M$ such that $e\cap M=\{m\}$ and for every $n\in M$, we have $(e\setminus
Externí odkaz:
http://arxiv.org/abs/2006.14527
Publikováno v:
In Discrete Mathematics October 2023 346(10)
Autor:
Bankoussou-mabiala, Edward, Boussaïri, Abderrahim, Chaïchaâ, Abdelhak, Chergui, Brahim, Lakhlifi, Soufiane
The idiosyncratic polynomial of a graph $G$ with adjacency matrix $A$ is the characteristic polynomial of the matrix $ A + y(J-A-I)$, where $I$ is the identity matrix and $J$ is the all-ones matrix. It follows from a theorem of Hagos (2000) combined
Externí odkaz:
http://arxiv.org/abs/1910.13914
An $n$-tournament $T$ with vertex set $V$ is simple if there is no subset $M$ of $V$ such that $2\leq \left \vert M\right \vert \leq n-1$ and for every $x\in V\setminus M$, either $M\rightarrow x$ or $x \rightarrow M$. The simplicity index of an $n$-
Externí odkaz:
http://arxiv.org/abs/1907.11777
This paper solves the following problem about Hermitian matrices related to the theory of $2$-structures:\emph{ }Let $n$ be a positive integer and $k$ be an integer with $k\in \{3,\ldots,n-3\}$. Characterize the Hermitian matrices $A$ such that the c
Externí odkaz:
http://arxiv.org/abs/1907.05817