Submatrices of non-tree-realizable distance matrices

Reconstruction of matrices from submatrices

For an arbitrary matrix A of n×n symbols, consider its submatrices of size k×k, obtained by deleting n−k rows and n−k columns. Optionally, the deleted rows and columns can be selected symmetrically or independently. We consider the problem of whether these multisets determine matrix A. Following the ideas of Krasikov and Roditty in the reconstruction of sequences from subsequences, we replace t...

On computing minimal realizable spectral radii of non-negative matrices

For decades considerable efforts have been exerted to resolve the inverse eigenvalue problem for nonnegative matrices. Yet fundamental issues such as the theory of existence and the practice of computation remain open. Recently it has been proved that, given an arbitrary (n − 1)-tuple L = (λ2, . . . , λn) ∈ C n−1 whose components are closed under complex conjugation, there exists a unique posit...

Submatrices of Four Dimensional Summability Matrices

In this paper, we show that a matrix that maps l ′′ into l ′′ can be obtained from any RH-regular matrix by the deletion of rows. Also a four dimensional conservative matrix can be obtained by the deletion of rows from a matrix that preserves boundedness. We will use these techniques to derive a sufficient condition for a four dimensional matrix to sum an unbounded sequence. RESUMEN En este tra...

Forbidden submatrices in 0-1 matrices

Submatrices of Hadamard matrices: complementation results

Two submatrices A,D of a Hadamard matrix H are called complementary if, up to a permutation of rows and columns, H = [