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.
The square
Hurwitz matrix associated to P is given below:
The i-th Hurwitz determinant is the i-th
leading principal minor (minor is a determinant) of the above Hurwitz matrix H. There are n Hurwitz determinants for a characteristic polynomial of degree n.
Hurwitz, A. (1895), "Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt", Mathematische Annalen, 46 (2): 273–284,
doi:
10.1007/BF01446812,
S2CID121036103