Concerning row operations on systems of linear equations with integral coefficients.
Conjugacy and factorization results on matrix groups
In this survey paper, we present (mainly without proof) a number of results on conjugacy and factorization in general linear groups over fields and commutative rings. We also present the additive analogue in matrix rings of some of these results. The first section deals with the question of expressing elements in the commutator subgroup of the general linear group over a field as (simple) commutators. In Section 2, the same kind of problem is discussed for the general linear group over a commutative...
Continued fractions and transformations of integer sequences.
Counting determinants of Fibonacci-Hessenberg matrices using LU factorizations.
Determinant Representations of Sequences: A Survey
This is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices. Some of these matrices are constructed by homogeneous or nonhomogeneous recurrence relations, and others are constructed by convolution of two sequences. In this article, we will illustrate the idea of these methods by constructing some integer matrices of this...
Directed graphs and matrix equations
Distribution of values of permanent and standard forms of (0,1)-matrices
Divisibility properties of Smith matrices
Eine homologische Interpretation gewisser Inzidenzmatrizen mod p.
Enumerating non-equivalent matrices over principal ideal domains
Evaluation of divisor functions of matrices
1. Introduction. The study of divisor functions of matrices arose legitimately in the context of arithmetic of matrices, and the question of the number of (possibly weighted) inequivalent factorizations of an integer matrix was asked. However, till now only partial answers were available. Nanda [6] evaluated the case of prime matrices and Narang [7] gave an evaluation for 2×2 matrices. We obtained a recursion in the size of the matrices and the weights of the divisors [1,2] which helped us obtain...
Explicit inverse of the Pascal matrix plus one.
Exponential Riordan arrays and permutation enumeration.
Extension of Partial Diagonals of Matrices II.
Factorization of matrices associated with classes of arithmetical functions
Let f be an arithmetical function. A set S = x₁,..., xₙ of n distinct positive integers is called multiple closed if y ∈ S whenever x|y|lcm(S) for any x ∈ S, where lcm(S) is the least common multiple of all elements in S. We show that for any multiple closed set S and for any divisor chain S (i.e. x₁|...|xₙ), if f is a completely multiplicative function such that (f*μ)(d) is a nonzero integer whenever d|lcm(S), then the matrix having f evaluated at the greatest common divisor of and as its...
Fermat's Equation in Matrices
The Fermat equation is solved in integral two by two matrices of determinant one as well as in finite order integral three by three matrices.
Gcd-closed sets and determinants of matrices associated with arithmetical functions
Generalized Catalan numbers, Hankel transforms and Somos-4 sequences.
Generalized indices of Boolean matrices
We obtain upper bounds for generalized indices of matrices in the class of nearly reducible Boolean matrices and in the class of critically reducible Boolean matrices, and prove that these bounds are the best possible.
Generalized Pascal -eliminated functional matrix with variables.