منابع مشابه
Orbit Closures of Singular Matrix Pencils
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...
متن کاملHierarchy of closures of matrix pencils
The focus of this paper is the standard linear representation of the group SLn(C)×SLm(C)×SL2(C), that is, the tensor product of the corresponding tautological representations. Classification of its orbits is a classic problem, which goes back to the works of Kronecker and Weierstrass. Here, we summarize some known results about standard linear representations of SLn(C) × SLm(C) × SL2(C), GLn(C)...
متن کاملOn 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...
متن کاملOn the closures of orbits of fourth order matrix pencils
In this work we state a simple criterion for nilpotentness of a square n×n matrix pencil with respect to the action of SLn(C)×SLn(C)×SL2(C). The orbits of matrix pencils are classified explicitly for n = 4 and the hierarchy of closures of nilpotent orbits is described. Also, we prove that the algebra of invariants of the action of SLn(C)× SLn(C)× SL2(C) on C ⊗ C ⊗ C is isomorphic to the algebra...
متن کاملOrbit Closure Hierarchies of Skew-symmetric Matrix Pencils
We study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skewsymmetric matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another ske...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1992
ISSN: 0022-4049
DOI: 10.1016/0022-4049(92)90002-w