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      Canonical Forms for Matrices over Polynomial Rings

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      NEYE-THESIS-2017.pdf (612.4Kb)
      Date
      2017-09-20
      Author
      Neye, Emmanuel O 1991-
      Type
      Thesis
      Degree Level
      Masters
      Metadata
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      Abstract
      One of the important concepts in matrix algebra is rank of matrices. If the entries of such matrices are from fields or principal ideal domains, then this concept of rank is well-defined. However, when such matrices are defined over the ring of polynomials F[x_1, . . . , x_k ], k ≥ 2 (polynomial matrices in more than one indeterminate), the concept of rank has different but inequivalent definitions. Despite this flaw, some theories, in relation to ranks, can still be applied to polynomial matrices in more than one indeterminate. One of the outcomes of these theories is that lower and upper bounds for ranks of such polynomial matrices in more than one indeterminate can be obtained. Just like matrices over fields or principal ideal domains can be reduced to some simpler or canonical forms, there are algorithms that can be used to reduce matrices over polynomial rings in more than one indeterminate to some simpler forms, though these reduced forms do not always tell the ranks of such polynomial matrices in more than one indeterminate. In this thesis, these algorithms will be presented with examples.
      Degree
      Master of Science (M.Sc.)
      Department
      Mathematics and Statistics
      Program
      Mathematics
      Supervisor
      Bremner, Murray
      Committee
      Samei, Ebrahim; Rajchgot, Jenna; Keil, Mark
      Copyright Date
      August 2017
      URI
      http://hdl.handle.net/10388/8117
      Subject
      rank of polynomial matrices in more than one indeterminate
      lower and upper bounds for ranks of polynomial matrices
      simpler or canonical forms for polynomial matrices
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