High Quality Content by WIKIPEDIA articles! In mathematics, Routh–Hurwitz theorem gives a test to determine whether a given polynomial is Hurwitz-stable. It was proved in 1895 and named after Edward John Routh and Adolf Hurwitz.From the first equality we can for instance conclude that when the variation of the argument of f(iy) is positive, then f(z) will have more roots to the left of the imaginary axis than to its right. The equality p-q=w(+?)-w(-?) can be viewed as the complex counterpart of Sturm's theorem. Note the differences: in Sturm's theorem, the left member is p+q and the w from the right member is the number of variations of a Sturm chain (while w refers to a generalized Sturm chain in the present theorem).

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