A New Formulation of the Theorems of Hurwitz, Routh and Sturm

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Abstract
It is shown that the Hurwitz determinants associated with a real polynomial of degree n can be obtained from minors of matrices having orders n/2 or (n—1)/2 according as n is even or odd. The method used is based on forming companion matrices of appropriate polynomials, and is extended to calculation of Routh arrays, Sturm sequences and to complex polynomials, thus providing a new formulation of a number of classical theorems.

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