Normal forms in matrix spaces

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19 Scopus citations

Abstract

For the group GL(m, C) × GL(n, C) acting on the space of m × n matrices over C, we introduce a class of subgroups which we call admissible. We suggest an algorithm to reduce an arbitrary matrix to a normal form with respect to an action of any admissible group. This algorithm covers various classification problems, including the "wild problem" of bringing a pair of matrices to normal form by simultaneous similarity. The classical left, right, two-sided and similarity transformations turns out to be admissible. However, the stabilizers of known normal forms (Smith's, Jordan's), generally speaking, are not admissible, and this obstructs inductive steps of our algorithm. This is the reason that we introduce modified normal forms for classical actions.

Original languageEnglish
Pages (from-to)251-283
Number of pages33
JournalIntegral Equations and Operator Theory
Volume38
Issue number3
DOIs
StatePublished - 1 Jan 2000

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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