Greatest Common Divisors via Generalized Sylvester and Bezout Matrices

R. R. Bitmead, S. Y. Kung, B. D.O. Anderson, T. Kailath

Research output: Contribution to journalArticlepeer-review

140 Scopus citations


We present new methods for computing the greatest common right divisor of polynomial matrices. These methods involve the recently studied generalized Sylvester and generalized Bezoutian resultant matrices, which require no polynomial operations. They can provide a row proper greatest common right divisor, test for coprimeness and calculate dual dynamical indices. The generalized resultant matrices are developments of the scalar Sylvester and Bezoutian resultants and many of the familiar properties of these latter matrices are demonstrated to have analogs with the properties of the generalized resultant matrices for matrix polynomials.

Original languageEnglish (US)
Pages (from-to)1043-1047
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - Dec 1978
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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