Bounds for the distance between nearby Jordan and Kronecker structures in a closure hierachy (Q1405645)

The paper deals with the following problem: what are the nearby canonical structures of a matrix or a matrix pencil? The authors present lower and upper bounds for the distance between Jordan and Kronecker structures in a closure hierarchy of an orbit or bundle stratification. Their upper bounds are based on staircase regularizing perturbations. The lower bounds are of Eckart-Young type and are derived from a matrix representation of the tangent space of the orbit of a matrix or a matrix pencil. The authors also present computational results that illustrate the use and reliability of the bounds.