相关论文: Results about persymmetric matrices over F_2 and r…

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

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

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)

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)

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 count the number of some particular sextuple 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.

Over the finite field with two elements, we present a method for obtaining explicit expressions for the number of rank i matrices of the form A above B, where A is persymmetric (A matrix [a(i,j)] is persymmetric if a(i,j) = a(r,s) for i+j =…

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.

We prove that the range of a symmetric matrix over F_2 contains the vector of its diagonal elements. We apply the theorem to a generalization of the "Lights Out" problem on graphs.

We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This…

We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…

This paper is divided into two parts. In the first part, we develop a general method for expressing ranks of matrix expressions that involve Moore-Penrose inverses, group inverses, Drazin inverses, as well as weighted Moore-Penrose inverses…

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…

Random linear systems over the Galois Field modulo 2 have an interest in connection with problems ranging from computational optimization to complex networks. They are often approached using random matrices with Poisson-distributed or…

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…

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…