Inverse spectral problem for normal matrices and the Gauss-Lucas theorem
نویسندگان
چکیده
منابع مشابه
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 roots of a complex polynomial and its derivative and an analog of Rol...
متن کاملInverse 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...
متن کاملAn inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem
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 re...
متن کاملthe algorithm for solving the inverse numerical range problem
برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
15 صفحه اولThe Gauss-lucas Theorem and Jensen Polynomials
A characterization is given of the sequences {"fyj^o vvith the property that, for any complex polynomial/(z) = 1akzk and convex region Kcontaining the origin and the zeros of/, the zeros of 2 y¡<akzk again lie in K. Many applications and related results are also given. This work leads to a study of the Taylor coefficients of entire functions of type I in the Laguerre-Pólya class. If the power s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2004
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-04-03649-9