Geodesic
On the minimal coset coverings of the set of singular and of the set of nonsingular matrices
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 52 (2018) no. 1, pp. 8-11

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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
Mots-clés : matrices. 
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     title = {On the minimal coset coverings of the set of singular and of the set of nonsingular matrices},
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A. V. Minasyan. On the minimal coset coverings of the set of singular and of the set of nonsingular matrices. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 52 (2018) no. 1, pp. 8-11. http://geodesic.mathdoc.fr/item/UZERU_2018_52_1_a1/