Inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem

Details Inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem Inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem

2003-04-12

arxiv.org/abs/math/0304158v3

Mathematics

Complex Variables

typos corrected; references added

Scientific paper

We estabish 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 (Borg-type 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.

Affiliated with

Also associated with

No associations

Rating

Inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-190068