This paper studies the set of n × n matrices for which all row and column sums equal zero. By representing these matrices in a lower dimensional space, it is shown that this set is closed under addition and multiplication, and furthermore is isomorphic to the set of arbitrary (n−1)×(n−1) matrices. The Moore-Penrose pseudoinverse corresponds with the true inverse, (when it exists), in this lower...

Recently, Jeĺınek derived that the number of self-dual interval orders of reduced size n is twice the number of row-Fishburn matrices of size n by using generating functions. In this paper, we present a bijective proof of this relation by establishing a bijection between two variations of upper-triangular matrices of nonnegative integers. Using the bijection, we provide a combinatorial proof of...

Let d = (d1, d2, . . . , dn) be a vector of nonnegative integers. We study the number of symmetric 0-1 matrices whose row sum vector equals d. While previous work has focussed on the case of zero diagonal, we allow diagonal entries to equal 1. Specifically, for D ∈ {1, 2} we define the set GD(d) of all n × n symmetric 0-1 matrices with row sums given by d, where each diagonal entry is multiplie...

In this paper we consider the problem of estimating simultaneously low-rank and row-wise sparse matrices from nested linear measurements where the linear operator consists of the product of a linear operatorW and a matrix Ψ . Leveraging the nested structure of the measurement operator, we propose a computationally efficient two-stage algorithm for estimating the simultaneously structured target...