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...

In this paper we present an efficient approach for comparing protein structures based on distance matrices. In the first step, the distance matrices are calculated and normalized in order to avoid the scaling distortion. Further, versions from these matrices are saved on different scales and for each two protein structures we compare their respective equal-scaled matrices. Thus, we avoid the pr...

j, 1 i 2n, 1 j 2n, where J2n is the 2n by 2n matrix of all entries 1. It is known that symmetric Bush–type Hadamard matrices exist for all orders 16n2 for all values of n for which there is a Hadamard matrix of order 4n, see [8] for details. A balanced generalized weighing matrix BGW ν κ λ over a group G is a matrix W wi j of order ν , with wi j G 0 such that each row and column of W has κ non–...

We study a natural random walk over the upper triangular matrices, with entries in the field Z2, generated by steps which add row i + 1 to row i. We show that the mixing time of the lazy random walk is O(n) which is optimal up to constants. Our proof makes key use of the linear structure of the group and extends to walks on the upper triangular matrices over the fields Zq for q prime.

The paper presents a subspace type of identification method for multivariable linear parameter-varying systems in state space representation with affine parameter dependence. It is shown that a major problem with subspace methods for this kind of systems is the enormous dimensions of the data matrices involved. To overcome the curse of dimensionality, we suggest to use only the most dominant ro...

$R_+^{n\times n}$ denotes the set of $n\times n$ non-negative matrices. For $A\in R_+^{n\times let $\Omega(A)$ be all matrices that can formed by permuting elements within each row $A$. Formally: $$\Omega(A)=\{B\in n}: \forall i\;\exists\text{ a permutation }\phi_i\; \text{s.t.}\ b_{i,j}=a_{i,\phi_i(j)}\;\forall j\}.$$ $B\in\Omega(A)$ $\rho(B)$ denote spectral radius or largest non negative eig...

A permuted graph matrix is a matrix V ∈ C(m+n)×m such that every row of the m×m identity matrix Im appears at least once as a row of V . Permuted graph matrices can be used in some contexts in place of orthogonal matrices, for instance when giving a basis for a subspace U ⊆ Cm+n, or to normalize matrix pencils in a suitable sense. In these applications the permuted graph matrix can be chosen wi...