User:DVD206/Special matrices and determinants

Special matrices, Hurwitz matrices, continued fractions,

given a real polynomial
 * $$p(z)=z^n+a_{1}z^{n-1}+\cdots+a_{n-1}z+a_n$$

the $$n\times n$$ square matrix
 * $$ H(p) := \begin{bmatrix}

a_1 & a_3 & a_5 & a_7 & \ldots & 0\\ 1 & a_2 & a_4 & a_6& \ldots & 0\\ 0 & a_1 & a_3 & a_5& \ldots & 0\\ 0 & 1 & a_2 & a_4& \ldots & 0\\ 0 & 0 & a_1 & a_3& \ldots & 0\\ \vdots & \vdots & \vdots & \vdots& \ddots& \vdots\\ 0 & 0 & 0 & 0& \ldots& a_n\\ \end{bmatrix}$$ is called Hurwitz matrix corresponding to the polynomial $$p$$.