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A method to determine whether two polynomials are relatively prime

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2 Author(s)
W. Vogt ; University of Pittsburgh, Pittsburgh, PA, USA ; N. Bose

In this paper, it is established that a necessary and sufficient condition for two monic polynomials f(\lambda ) and g(\lambda ) to have a common root is that \det [f(B)] = 0 or \det [g(A)] = 0 , where A and B are, respectively, the companion matrices associated with f(\lambda ) and g(\lambda ) . The simplicity of this method is illustrated by examples.

Published in:

IEEE Transactions on Automatic Control  (Volume:15 ,  Issue: 3 )