Related papers: Exponential sums and rank of persymmetric matrices…

We obtain using exponential quadratic sums, explicit expressions for the number of triple persymmetric matrices over F_2 of given rank. (A matrix [a(i,j)] is persymmetric if a(i,j) = a(r,s) for i+j = r+s)

We obtain, using exponential quadratic sums, explicit expressions for the number of double persymmetric matrices with entries in F_2 of given rank. (A matix [a(i,j)) is persymmetric if a(i,j) = a(r,s) for i+j = r+s)

In this paper we count the number of some particular quadruple persymmetric rank i matrices over F_2.

In this paper we count the number of some particular quintuple persymmetric rank i matrices over F_2.

In this paper we count the number of some particular sextuple persymmetric rank i matrices over F_2.

In this paper we count the number of some particular n-times persymmetric rank i matrices over F_2.

In this paper we expose our main results about rank problems concerning persymmetric matrices over F_2 associated to some exponential sums.

In this paper we count the number of some particular 2n x 9 n-times rank i matrices over F_2.

In this paper we count the number of some particular 2nx10 n-times rank i matrices over F_2.

In this paper we illustrate by some examples the connection between the number of solutions of polynomial equations satisfying degree conditions and the number of rank I matrices related to persymmetric matrices.

In this paper we announce a conjecture concerning enumeration of n-times persymmetric matrices over F_2 by rank. To justify our statement we remark that the formulas obtained are valid for n equal to one, two and three.

In this paper we announce a conjecture concerning enumeration of 2n x k n-times persymmetric matrices over F_2 by rank.

In the present article we shown a formula to compute the number of all matrices over the finite field $F$ whit prescribed eigenvalues. Using this formula we obtain one inequality for the number of $(k+1)$-potent elements over finite rings.

Motivated by recent works on statistics of matrices over sets of number theoretic interest, we study matrices with entries from arbitrary finite subsets $\mathcal A$ of finite rank multiplicative groups infields of characteristic zero. We…

The paper explores the concept of the rank of a bicomplex matrix, delving into four distinct types of ranks and investigating conditions under which these ranks are equivalent. It also defines and analyzes the concept of idempotent row…

We study the maximal rank in affine subspaces of symmetric or alternating matrices, in terms of the matching numbers of certain associated graphs. Applications include simple proofs of upper bounds on the dimension of such subspaces in…

For every $n \in \mathbb{N}$ and every field $K$, let $A(n,K)$ be the vector space of the antisymmetric $(n \times n)$-matrices over $K$. We say that an affine subspace $S$ of $A(n,K)$ has constant rank $r$ if every matrix of $S$ has rank…

In this paper, we study the rank of matrices of bicomplex numbers. The relationship between rank, idempotent column rank and idempotent row rank is examined. Then, the solution of a system of equations in bicomplex space is presented using…

We study characteristic polynomials of symmetric matrices with entries ${i+j\choose i}$ the binomial coefficients, over finite fields.

We show that the sum of ranks of two matrix polynomials is the same as the sum of the rank of the matrix obtained by applying the greatest common divisor of the polynomials, with the rank of the matrix obtained by applying the lowest common…