Finding positive matrices subject to linear restrictions

The Reparameterization of Linear Models Subject to Exact Linear Restrictions

The estimation of regression models subject to exact linear restrictions, is a widely applied technique, however, aside from simple examples, the reparameterization method is rarely employed except in the case of polynomial lags. We believe this is due to the lack of a general transformation method for changing from the definition of restrictions in terms of the unrestricted parameters to the e...

Totally Positive Density Matrices and Linear Preservers

The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated. The single qubit case is characterized, and several equivalent conditions for a quantum channel to preserve the set in that case are given. Hig...

Positive Linear Maps and Spreads of Matrices

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

Real root finding for determinants of linear matrices

Let A0, A1, . . . , An be given square matrices of size m with rational coefficients. The paper focuses on the exact computation of one point in each connected component of the real determinantal variety {x ∈ Rn : det(A0 +x1A1 + · · ·+xnAn) = 0}. Such a problem finds applications in many areas such as control theory, computational geometry, optimization, etc. Using standard complexity results t...