Narayana, Mandelbrot, and A New Kind of Companion Matrix

Eunice Y. S. Chan, Robert M. Corless

We demonstrate a new kind of companion matrix, for polynomials of the form $c(\lambda )=\lambda a(\lambda )b(\lambda )+c_0$ where upper Hessenberg companions are known for the polynomials $a(\lambda )$ and $b(λ)…