We give a formulation, via (1, 1) matrices, of Mathon's construction for conference matrices and derive a new family of conference matrices of order 5·92r+1 + 1, t ≥ 0. This family produces a new conference matrix of order 3646 and a new Hadamard matrix of order 7292. In addition we construct new families of Hadamard matrices of orders 6.92r+1+ 2, 10.92t+1 + 2, 8·49·92, t ≥ 0; q2(q + 3) + 2 whe...

We give a framework for formal orthogonal polynomials with respect to an arbitrary moment matrix. When the moment matrix is Hankel, this simplifies to the classical framework. The relation with Padé approximation and with Krylov subspace methods is given. 1 Formal block orthogonal polynomials We consider a linear functional defined on the space of polynomials in two variables, defined by the mo...

We analyze the spectral problem for the q-Knizhnik-Zamolodchikov equations for Uq(ŝl2)(0 < q ≤ 1) at level zero. The case of 2-point functions in the fundamental representation is studied in detail. The scattering states are found explicitly in terms of continuous q-Jacobi polynomials. The corresponding S-matrix is shown to coincide, up to a trivial factor, with the kink-antikink S-matrix in th...

Let B be an m × n (m ≥ n) complex (or real) matrix. It is known that there is a unique polar decomposition B = QH, where Q * Q = I, the n × n identity matrix, and H is positive definite, provided B has full column rank. If B is perturbed to B, how do the polar factors Q and H changes? This question has been investigated quite extensively, but most work so far was on how the perturbation changed...

The linear complementarity problem (q,A) with data A ∈ Rn×n and q ∈ Rn involves finding a nonnegative z ∈ Rn such that Az+ q ≥ 0 and zt(Az+ q) = 0. Cottle and Stone introduced the class of P1-matrices and showed that if A is in P1\Q, then K(A) (the set of all q for which (q,A) has a solution) is a half-space and (q,A) has a unique solution for every q in the interior of K(A). Extending the resu...

On the half line 0; 1) we study rst order diierential operators of the form B 1 i d dx + Q(x); where B := B 1 0 0 ?B 2 ; B 1 ; B 2 2 M(n; C) are self{adjoint positive deenite matrices and Q : R + ! M(2n; C); R + := 0; 1); is a continuous self{adjoint oo{diagonal matrix function. We determine the self{adjoint boundary conditions for these operators. We prove that for each such boundary value pro...

The information of interest is contained in the variance matrix, σ − = 2 1 V Q , or equivalently in the information matrix Q . The problem of finding estimators minimizing a decreasing convex functional of the variance matrix or maximizing an increasing concave functional of the information matrix is crucial in statistics. There are several optimality criteria in bibliography. We explain how th...

The observation of neutrino oscillations requires new physics beyond the standard model (SM). A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU(2)L×U(1)Y gauge symmetry. The overall neutrino mass matrix M turns out to be a symmetric (p+q)×(p+q) matrix. Given p > q, the rank of M is in general equal to 2q, c...

Diagnostic classification models have recently gained prominence in educational assessment, psychiatric evaluation, and many other disciplines. Central to the model specification is the so-called Q-matrix that provides a qualitative specification of the item-attribute relationship. In this paper, we develop theories on the identifiability for the Q-matrix under the DINA and the DINO models. We ...

In this paper, the relationship between the (P,Q)-orthogonal symmetric and symmetric matrices is derived. By applying the generalized singular value decomposition, the general expression of the least square (P,Q)-orthogonal symmetric solutions for the matrix equation AXB = C is provided. Based on the projection theorem in inner space, and by using the canonical correlation decomposition, an ana...