Inverse spectral problem for normal matrices and the Gauss-Lucas theorem
Semyon Malamud · Transactions of the American Mathematical Society · 2004
We establish an analog of the Cauchy-Poincare interlacing theorem for normal matrices in terms of majorization, and we provide a solution to the corresponding inverse spectral problem. Using this solution we generalize and extend the Gauss–Lucas theorem and prove the old conjecture of de Bruijn-Springer on the location of the roots of a complex polynomial and its derivative and an analog of Rolle’s theorem, conjectured by Schoenberg.