Hurwitz determinant
Encyclopedia
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.
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 principal minor of the above Hurwitz matrix H. There are n Hurwitz determinants for a characteristic polynomial of degree n.
Definition
Let us consider a characteristic polynomialCharacteristic polynomial
In linear algebra, one associates a polynomial to every square matrix: its characteristic polynomial. This polynomial encodes several important properties of the matrix, most notably its eigenvalues, its determinant and its trace....
P in the variable λ of the form:
where
, , are real.The square Hurwitz matrix
Hurwitz matrix
-Hurwitz matrix and the Hurwitz stability criterion:In mathematics, Hurwitz matrix is a structured real square matrix constructed with coefficientsof a real polynomial...
associated to P is given below:
The ith Hurwitz determinant is the determinant of the ith principal minor of the above Hurwitz matrix H. There are n Hurwitz determinants for a characteristic polynomial of degree n.