Determinants of nonprincipal submatrices of normal 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...

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...

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 = [

Rank-deficient submatrices of Fourier matrices

We consider the maximal rank-deficient submatrices of Fourier matrices. We do this by considering a hierarchical subdivision of these matrices into low rank blocks. We also explore some connections with the FFT, and with an uncertainty principle for Fourier transforms over finite Abelian groups.

Forbidden submatrices in 0-1 matrices