Recently, a classi cation of matrices of class Z was introduced by Fiedler and Markham. This classi cation contains the classes ofM{matrices and the classes of N0 and F0{matrices studied by K. Fan, G. Johnson, and R. Smith. The problem of determining which nonsingular matrices have inverses which are Z{matrices is called the inverse Z{matrix problem. For special classes of Z{ matrices, such as ...

Under certain assumptions we show that a wavelet frame {τ(Aj , bj,k)ψ}j,k∈Z := {|detAj |−1/2ψ(A−1 j (x− bj,k))}j,k∈Z in L2(Rd) remains a frame when the dilation matrices Aj and the translation parameters bj,k are perturbed. As a special case of our result, we obtain that if {τ(Aj , ABn)ψ}j∈Z,n∈Zd is a frame for an expansive matrix A and an invertible matrix B, then {τ(Aj , ABλn)ψ}j∈Z,n∈Zd is a ...

Here we discuss the “shifted” equivalence class of binary matrices first proposed by Ding et al. (2010). For a given N ×K binary matrix Z, the equivalence class for this binary matrix [Z] is obtained by shifting allzero columns to the right of the non-zero columns while maintaining the non-zero column orderings, see Figure 1. Placing independent Beta( α K , 1) priors on the Bernoulli entries of...

In this paper we study the inversion of an analytic matrix valued function A(z). This problem can also be viewed as an analytic perturbation of the matrix A 0 = A(0). We are mainly interested in the case where A 0 is singular but A(z) has an inverse in some punctured disc around z = 0. It is known that A ?1 (z) can be expanded as a Laurent series at the origin. The main purpose of this paper is...

We consider the linear complementarity problem (LCP): Mz + q ≥ 0, z ≥ 0, z′(Mz + q) = 0 as an absolute value equation (AVE): (M + I)z + q = |(M − I)z + q|, where M is an n× n square matrix and I is the identity matrix. We propose a concave minimization algorithm for solving (AVE) that consists of solving a few linear programs, typically two. The algorithm was tested on 500 consecutively generat...

The P, Z, and S properties of a linear transformation on a Euclidean Jordan algebra are generalizations of the corresponding properties of a square matrix on R. Motivated by the equivalence of P and S properties for a Z-matrix [2] and a similar result for Lyapunov and Stein transformations on the space of real symmetric matrices [6], [5], in this paper, we present two results supporting the con...

We study the eigendecompositions of para-Hermitian matrices H(z), that is, matrix-valued functions are analytic and Hermitian on unit circle S1?C. In particular, we fill existing gaps in literature prove existence a decomposition H(z)=U(z)D(z)U(z)P where, for all z?S1, U(z) is unitary, U(z)P=U(z)? its conjugate transpose, D(z) real diagonal; moreover, w=z1/N some positive integer N, U(z)P so-ca...

A new approach is described, for extracting and visualising structures in a data matrix Y in light of additional information BOTH about the ROWS in Y, given in matrix X, AND about the COLUMNS in Y, given in matrix Z. The three matrices Z–Y–X may be envisioned as an “L-shape”; X(I × K) and Z(J × L) share no matrix size dimension, but are connected via Y(I × J ). A few linear combinations (compon...

The S-matrix in the static limit of a dispersion relation is a matrix of a finite order N of meromorphic functions of energy ω in the plane with cuts (−∞,−1], [+1,+∞). In the elastic case it reduces to N functions Si(ω) connected by the crossing symmetry matrix A. The scattering of a neutral pseodoscalar meson with an arbitrary angular momentum l at a source with spin 1/2 is considered (N=2). T...