MATHEMATICAL ENGINEERING TECHNICAL REPORTS On Kronecker Canonical Form of Mixed Matrix Pencils
نویسندگان
چکیده
A mixed matrix pencil is a matrix pencil which has two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. In this paper, we characterize the indices of nilpotency of the Kronecker canonical form for a mixed matrix pencil in terms of matroids. As a byproduct, we provide an algorithm for computing the rank of a power product of a square mixed matrix.
منابع مشابه
MATHEMATICAL ENGINEERING TECHNICAL REPORTS Combinatorial Analysis of Generic Matrix Pencils
This paper investigates the Kronecker canonical form of matrix pencils under the genericity assumption that the set of nonzero entries is algebraically independent. We provide a combinatorial characterization of the sums of the row/column indices supported by efficient bipartite matching algorithms. We also give a simple alternative proof for a theorem of Poljak on the generic ranks of matrix p...
متن کاملOn the Kronecker Canonical Form of Singular Mixed Matrix Pencils
Dynamical systems, such as electric circuits, mechanical systems, and chemical plants, can be modeled by mixed matrix pencils, i.e., matrix pencils having two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. Based on dimension analysis of dynamical systems, Murota (1985) introduced a physically ...
متن کاملThe Quasi-Kronecker Form For Matrix Pencils
We study singular matrix pencils and show that the so called Wong sequences yield a quasi-Kronecker form. This form decouples the matrix pencil into an underdetermined part, a regular part and an overdetermined part. This decoupling is sufficient to fully characterize the solution behaviour of the differential-algebraic equations associated with the matrix pencil. Furthermore, the Kronecker can...
متن کاملA Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations∗
We derive versal deformations of the Kronecker canonical form by deriving the tangent space and orthogonal bases for the normal space to the orbits of strictly equivalent matrix pencils. These deformations reveal the local perturbation theory of matrix pencils related to the Kronecker canonical form. We also obtain a new singular value bound for the distance to the orbits of less generic pencil...
متن کاملA Structured Staircase Algorithm for Skew-symmetric/symmetric Pencils
A STRUCTURED STAIRCASE ALGORITHM FOR SKEW-SYMMETRIC/SYMMETRIC PENCILS RALPH BYERS , VOLKER MEHRMANN , AND HONGGUO XU Abstract. We present structure preserving algorithms for the numerical computation of structured staircase forms of skew-symmetric/symmetric matrix pencils along with the Kronecker indices of the associated skew-symmetric/symmetric Kronecker-like canonical form. These methods all...
متن کامل