Hurwitz determinant

In mathematics, Hurwitz determinants were introduced by , who used them to give a criterion for all roots of a polynomial to have negative real part.
Definition.
Consider a characteristic polynomial "P" in the variable "λ" of the form:
where formula_2, formula_3, are real.
The square Hurwitz matrix associated to "P" is given below:
The "i"th "Hurwitz determinant" is the determinant of the "i"th leading principal minor of the above Hurwitz matrix "H". There are "n" Hurwitz determinants for a characteristic polynomial of degree "n".