This paper describes structural properties of solutions to distance problems for rectangular matrix pencils. Properties are given for both the closest non-generic pencil and the smallest perturbation which yields a non-generic pencil. Smoothness results are given which suggest a natural geometric understanding of the problem and allow extension to more general distance problems.

In this paper, we propose a method for finding certain eigenvalues of a generalized eigenvalue problem that lie in a given domain of the complex plane. The proposed method projects the matrix pencil onto a subspace associated with the eigenvalues that are located in the domain via numerical integration. The projection produces a small pencil with Hankel matrices.

In the present work, under some di¤erentiability conditions on the potential functions , we …rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...

Computing the ne canonical-structure elements of matrices and matrix pencils are ill-posed problems. Therefore, besides knowing the canonical structure of a matrix or a matrix pencil, it is equally important to know what are the nearby canonical structures that explain the behavior under small perturbations. Qualitative strata information is provided by our StratiGraphtool. Here, we present low...

Using two diierent matrix pencil descriptions two new classes of convolutional codes with designed lower free distance are introduced.

The matrix pencil algebraic characterisation of the families of invariant subspaces of an implicit system S(F, G) : Fz = Gz F, G € K m x n , is further developed by using tools from Exterior Algebra and in particular the Grassmann Representative g(V) of the subspace V of the domain of (F,G). Two different approaches are considered: The first is based on the compound of the pencil C'd(sF — G), w...

Let A(x) = A0 + x1A1 + · · · + xnAn be a linear matrix, or pencil, generated by given symmetric matrices A0, A1, . . . , An of size m with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a convex semialgebraic set called spectrahedron, described by a linear matrix inequality (LMI). We design an exact algorithm that, up to genericity assumptions on th...

To understand the solution of a linear, time-invariant differential-algebraic equation (DAE), one must analyze a matrix pencil (A,E) with singular E. Even when this pencil is stable (all its finite eigenvalues fall in the left half-plane), the solution can exhibit transient growth before its inevitable decay. When the equation results from the linearization of a nonlinear system, this transient...