Hurwitz determinant

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In mathematics, Hurwitz determinants were introduced by Adolf Hurwitz (1895), who used them to give a criterion for all roots of a polynomial to have negative real part.


Let us consider a characteristic polynomial P in the variable λ of the form:

where , , are real.

The square Hurwitz matrix associated to P is given below:

The ith Hurwitz determinant is the determinant of the ith leading principal minor of the above Hurwitz matrix H. There are n Hurwitz determinants for a characteristic polynomial of degree n.

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