The gap distance to the set of singular matrix pencils
نویسندگان
چکیده
منابع مشابه
On generalized inverses of singular matrix pencils
Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate s...
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The stability analysis of dynamical systems leads to the eigenstructure analysis of matrix pencils λE−A. The associated system is asymptotically stable if the pencil is regular, all finite eigenvalues are in the left half plane and the infinite eigenvalues are semisimple. There are several challenging open problems that will be discussed. The first is the distance to instability, i.e. the small...
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Equivalence of matrix pencils (pairs of pq matrices over C) is given by the GL p GL q-action of simultaneous left and right multiplication. The orbits under this group action were described by Kronecker in 1890 in terms of pencil invariants: column indices, row indices, and elementary divisors. In this paper we describe the topological closures of these orbits, a problem motivated by our work i...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2019
ISSN: 0024-3795
DOI: 10.1016/j.laa.2018.11.020