An inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem
نویسندگان
چکیده
We estabish an analog of the Poincare-Cauchy separation theorem for normal matrices in terms of majorization. Moreover, we present a solution to the inverse spectral problem (Borgtype result) for a normal matrix. Using this result we essentially generalize and complement the known Gauss–Lucas theorem on the geometry of the roots of a complex polynomial and of its derivative. In turn the last result is applied to prove the old conjectures of de Bruijn-Springer and Schoenberg about these roots.
منابع مشابه
Inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem
We establish an analog of the Cauchy-Poincare separation theorem for normal matrices in terms of majorization. Moreover, we present a solution to the inverse spectral problem (Borgtype result). Using this result we essentially generalize and extend the known Gauss–Lucas theorem about the location of the roots of a complex polynomial and of its derivative. The last result is applied to prove the...
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