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Special matrices, Hurwitz matrices , continued fractions,

given a real polynomial

${\displaystyle p(z)=z^{n}+a_{1}z^{n-1}+\cdots +a_{n-1}z+a_{n}}$

the ${\displaystyle n\times n}$ square matrix

${\displaystyle H(p):={\begin{bmatrix}a_{1}&a_{3}&a_{5}&a_{7}&\ldots &0\\1&a_{2}&a_{4}&a_{6}&\ldots &0\\0&a_{1}&a_{3}&a_{5}&\ldots &0\\0&1&a_{2}&a_{4}&\ldots &0\\0&0&a_{1}&a_{3}&\ldots &0\\\vdots &\vdots &\vdots &\vdots &\ddots &\vdots \\0&0&0&0&\ldots &a_{n}\\\end{bmatrix}}}$

is called Hurwitz matrix corresponding to the polynomial ${\displaystyle p}$.