On the Kronecker Canonical Form of Mixed Matrix Pencils

  • Authors:
  • Satoru Iwata;Mizuyo Takamatsu

  • Affiliations:
  • iwata@kurims.kyoto-u.ac.jp;takamatsu@ise.chuo-u.ac.jp

  • Venue:
  • SIAM Journal on Matrix Analysis and Applications
  • Year:
  • 2011

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Abstract

A mixed matrix pencil is a matrix pencil with two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. In this paper, the indices of nilpotency of the Kronecker canonical form for a mixed matrix pencil are characterized in terms of matroids. As a byproduct, this provides an algorithm for computing the rank of a power product of a square mixed matrix.