Ela Ranges of Sylvester Maps and a Minimal Rank Problem

Ranges of Sylvester maps and a minimal rank problem

Fast Low Rank Approximation of a Sylvester Matrix by Structured Total Least Norm

The problem of approximating the greatest common divisor(GCD) for polynomials with inexact coefficients can be formulated as a low rank approximation problem with a Sylvester matrix. In this paper, we present an algorithm based on fast Structured Total Least Norm(STLN) for constructing a Sylvester matrix of given lower rank and obtaining the nearest perturbed polynomials with exact GCD of given...

Ela Additive Rank–one Nonincreasing Maps on Hermitian Matrices over the Field

A complete classification of additive rank–one nonincreasing maps on hermitian matrices over Galois field GF (22) is obtained. This field is special and was not covered in a previous paper. As a consequence, some known applications, like the classification of additive rank–additivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieti...

Ela the Symmetric Minimal Rank Solution of the Matrix Equation Ax = B and the Optimal Approximation∗

By applying the matrix rank method, the set of symmetric matrix solutions with prescribed rank to the matrix equation AX = B is found. An expression is provided for the optimal approximation to the set of the minimal rank solutions.

Ela Numerical Ranges of Quadratic Operators in Spaces with an Indefinite Metric

The numerical range of a quadratic operator acting on an indefinite inner product space is shown to have a hyperbolical shape. This result is extended to different kinds of indefinite numerical ranges, namely, indefinite higher rank numerical ranges and indefinite Davis-Wielandt shells.