Inverse spectral problem for normal matrices and the Gauss-Lucas theorem
Inverse spectral problem for normal matrices and the Gauss-Lucas theorem
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 …