This article is cited in 2 papers

Mathematics

On the minimal coset coverings of the set of singular and of the set of nonsingular matrices

A. V. Minasyan

Chair of Discrete Mathematics and Theoretical Informatics YSU, Armenia

Abstract: It is determined minimum number of cosets over linear subspaces in $F_q$ necessary to cover following two sets of $A(n\times n)$ matrices. For one of the set of matrices $\det(A)=0$ and for the other set$\det(A)\neq 0$. It is proved that for singular matrices this number is equal to $1+q+q^2+\ldots+q^{n-1}$ and for the nonsingular matrices it is equal to $\dfrac{(q^n-1)(q^n-q)(q^n-q^2)\cdots(q^n-q^{n-1})}{q^{\binom{n}{2}}}$.

Keywords: linear algebra, covering with cosets, matrices.

MSC: Primary 97H60; Secondary 14N20, 51E21

Received: 21.12.2017
Accepted: 01.02.2018

Language: English