A GEOMETRIC APPROACH FOR TESTING REGULARITY OF MULTIDIMENSIONAL POLYNOMIAL-MATRICES AND A PENCIL OF NORMAL-MATRICES


SAVACI F., GOKNAR I.

KYBERNETIKA, vol.27, no.3, pp.271-279, 1991 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 3
  • Publication Date: 1991
  • Title of Journal : KYBERNETIKA
  • Page Numbers: pp.271-279

Abstract

In this paper, a geometric approach will be derived for testing column regularity (CR) of multi-dimensional (m-D) polynomial matrices and a pencil of n-matrices "n-pencil" using some spaces defined by the coefficient matrices of the polynomial matrices. Assigning x(Li) to multi-variable x(i) and using the form preserving polynomials concept it has been shown that CR of an n-pencil and m-D polynomial matrices can be stated as CR of a 1-D polynomial matrix. Defining an associated companion form for the 1-D polynomial matrix it has been proved that CR of 1-D polynomial matrix can be reduced to CR of the related 2-pencil. Thus CR of a m-D polynomial matrix and n-pencil has been stated in terms of CR of a pair of matrices.