The Euler-Fermat theorem for the semigroup of circulant Boolean matrices
The external vertices conjecture in case .
The factorization of an integral matrix into a product of two integral symmetric matrices I
The Frisch scheme in algebraic and dynamic identification problems
This paper considers the problem of determining linear relations from data affected by additive noise in the context of the Frisch scheme. The loci of solutions of the Frisch scheme and their properties are first described in the algebraic case. In this context two main problems are analyzed: the evaluation of the maximal number of linear relations compatible with data affected by errors and the determination of the linear relation actually linking the noiseless data. Subsequently the extension...
The general totally positive matrix completion problem with few unspecified entries.
The Hadamard product and related dilations
The Hankel transform and some of its properties.
The higher rank numerical range of nonnegative matrices
In this article the rank-k numerical range ∧k (A) of an entrywise nonnegative matrix A is investigated. Extending the notion of elements of maximum modulus in ∧k (A), we examine their location on the complex plane. Further, an application of this theory to ∧k (L(λ)) of a Perron polynomial L(λ) is elaborated via its companion matrix C L.
The inertia of Hermitian tridiagonal block matrices.
The inverse of the Pascal lower triangular matrix modulo .
The k-Fibonacci matrix and the Pascal matrix
We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.
The linear independence of sets of two and three canonical algebraic curvature tensors.
The local catenativity of DOL-sequences in free commutative monoids is decidable in the binary case
The local relaxation flow approach to universality of the local statistics for random matrices
We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues {xj}j=1N are close to their classical location {γj}j=1N determined by the limiting density of eigenvalues. Under...
The maximum multiplicity and the two largest multiplicities of eigenvalues in a Hermitian matrix whose graph is a tree
The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, M1, was understood fully (froma combinatorial perspective) by C.R. Johnson, A. Leal-Duarte (Linear Algebra and Multilinear Algebra 46 (1999) 139-144). Among the possible multiplicity lists for the eigenvalues of Hermitian matrices whose graph is a tree, we focus upon M2, the maximum value of the sum of the two largest multiplicities when the largest multiplicity is M1. Upper and lower bounds are given for M2. Using a combinatorial...
The maximum number of odd submatrices in -matrices.
The minimum, diagonal element of a positive matrix
Properties of the minimum diagonal element of a positive matrix are exploited to obtain new bounds on the eigenvalues thus exhibiting a spectral bias along the positive real axis familiar in Perron-Frobenius theory.
The nonnegative -matrix completion problem.
The number of matrix fields over GF(q)
The -matrix completion problem.