Routh–Hurwitz matrix
In mathematics, the Routh–Hurwitz matrix, or more commonly just Hurwitz matrix, corresponding to a polynomial is a particular matrix whose nonzero entries are coefficients of the polynomial. == Hurwitz matrix and the Hurwitz stability criterion == Namely, given a real polynomial p ( z ) = a 0 z n + a 1 z n − 1 + ⋯ + a n − 1 z + a n {\displaystyle p(z)=a_{0}z^{n}+a_{1}z^{n-1}+\cdots +a_{n-1}z+a_{n}} the n × n {\displaystyle n\times n} square matrix H = ( a 1 a 3 a 5 … … … 0 0 0 a 0 a 2 a 4 ⋮ ⋮ ⋮ 0 a 1 a 3 ⋮ ⋮ ⋮ ⋮ a 0 a 2 ⋱ 0 ⋮ ⋮ ⋮ 0 a 1 ⋱ a n ⋮ ⋮ ⋮ ⋮ a 0 ⋱ a n − 1 0 ⋮ ⋮ ⋮ 0 a n − 2 a n ⋮ ⋮ ⋮ ⋮ a n − 3 a n − 1 0 0 0 0 … … … a n − 4 a n − 2 a n ) .