Singular Values of Companion Matrices and Bounds on Zeros of Polynomials
Fuad Kıttaneh · SIAM Journal on Matrix Analysis and Applications · 1995
Let $C(p)$ denote the companion matrix of a monic polynomial p with complex coefficients. Then the zeros of p are exactly the eigenvalues of $C(p)$. In this paper, the singular values of $C(p)$ are computed. Applying some basic eigenvalue-singular value majorization relations, several sharp estimates are obtained for the zeros of p in terms of its coefficients. These estimates improve some classical bounds on zeros of polynomials.