Expressing a polynomial as the characteristic polynomial of a symmetric matrix
نویسندگان
چکیده
منابع مشابه
Symmetric Matrix Polynomial Equation
A new numerical procedure is proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal processing. It is based on interpolation and takes fully advantage of symmetry of the equation by reducing the original problem dimension. The algorithm is more eecient and more general than older methods and, namely, it...
متن کاملSymmetric matrix polynomial equations
For problems of linear control system synthesis, an apparatus of polynomial equations (for single-variable case) and of matrix polynomial equations (for multivariable case) was successfully developed in recent times, cf. [1]. In connection with quadratic criteria, we are led to equations of special type, containing an operation of conjugation ah-* a* representing a(s) i-> a( — s) for continuous...
متن کاملOn the Second-order Correlation Function of the Characteristic Polynomial of a Real Symmetric Wigner Matrix
Abstract We consider the asymptotic behaviour of the second-order correlation function of the characteristic polynomial of a real symmetric random matrix. Our main result is that the existing result for a random matrix from the Gaussian Orthogonal Ensemble, obtained by Brézin and Hikami [BH2], essentially continues to hold for a general real symmetric Wigner matrix. To obtain this result, we ad...
متن کاملSome Properties of the Characteristic Polynomial of a Nonnegative Matrix*
In this paper, we extend and generalize some of the well known spectral properties of a nonnegative matrix by establishing analogous properties for the zeros of derivatives of the characteristic polynomial of such a matrix.
متن کاملOn the Characteristic Polynomial of a Random Unitary Matrix
We present a range of fluctuation and large deviations results for the logarithm of the characteristic polynomial Z of a random N ×N unitary matrix, as N → ∞. First we show that lnZ/ √ 1 2 lnN , evaluated at a finite set of distinct points, is asymptotically a collection of i.i.d. complex normal random variables. This leads to a refinement of a recent central limit theorem due to Keating and Sn...
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: Linear Algebra and its Applications
سال: 1990
ISSN: 0024-3795
DOI: 10.1016/0024-3795(90)90323-5