Related papers: Classification problems for system of forms and li…

Hamiltonians are 2-by-2 positive semidefinite real symmetric matrix-valued functions satisfying certain conditions. In this paper, we solve the inverse problem for which recovers a Hamiltonian from the solution of a first-order system…

Building on the classification of all characteristic polynomials of integer symmetric matrices having small span (span less than 4), we obtain a classification of small-span polynomials that are the characteristic polynomial of a Hermitian…

We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries…

A good classification method should yield more accurate results than simple heuristics. But there are classification problems, especially high-dimensional ones like the ones based on image/video data, for which simple heuristics can work…

We consider the problem of removal of ordering ambiguity in position dependent mass quantum systems characterized by a generalized position dependent mass Hamiltonian which generalizes a number of Hermitian as well as non-Hermitian ordered…

The simple symplectic triple systems over the real numbers are classified up to isomorphism, and linear models of all of them are provided. Besides the split cases, one for each complex simple Lie algebra, there are two kinds of non-split…

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…

We give a canonical form of matrices of a cycle of linear or semilinear mapping V_1 --- V_2 --- ... --- V_t --- V_1 in which all V_i are complex vector spaces, each line is an arrow ---> or <---, and each arrow denotes a linear or…

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…

Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…

Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the…

We define geometric matrix midranges for positive definite Hermitian matrices and study the midrange problem from a number of perspectives. Special attention is given to the midrange of two positive definite matrices before considering the…

In 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions on a 5-dimensional manifold. We solve the analogous problems for rank 2 distributions on an n-dimensional…

This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…

The paper expands the theory of quadratic forms on modules over a semiring R, introduced in [12]-[14], especially in the setup of tropical and supertropical algebra. Isometric linear maps induce subordination on quadratic forms, and provide…

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…

In this paper we develop algorithms for orthogonal similarity transformations of skew-symmetric matrices to simpler forms. The first algorithm is similar to the algorithm for the block antitriangular factorization of symmetric matrices, but…

We establish a new symmetrization procedure for the isoperimetric problem in symmetric spaces of noncompact type. This symmetrization generalizes the well known Steiner symmetrization in euclidean space. In contrast to the classical…

We examine a family of 3-point mappings that include mappings solvable through linearization. The different origins of mappings of this type are examined: projective equations and Gambier systems. The integrable cases are obtained through…