On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values
نویسندگان
چکیده
Given any fixed N×N positive semi-definite diagonal matrix G ≥ 0 we derive the explicit formula for the density of complex eigenvalues for random matrices A of the form A = U √ G where the random unitary matrices U are distributed on the group U(N) according to the Haar measure.
منابع مشابه
استفاده از POD در استخراج ساختارهای متجانس یک میدان آشفته آماری- همگن
Capability of the Proper Orthogonal Decomposition (POD) method in extraction of the coherent structures from a spatio-temporal chaotic field is assessed in this paper. As the chaotic field, an ensemble of 40 snapshots, obtained from Direct Numerical Simulation (DNS) of the Kuramoto-Sivashinsky (KS) equation, has been used. Contrary to the usual methods, where the ergodicity of the field is need...
متن کاملComputational aspect to the nearest southeast submatrix that makes multiple a prescribed eigenvalue
Given four complex matrices $A$, $B$, $C$ and $D$ where $Ainmathbb{C}^{ntimes n}$ and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc} A & B C & D end{array} right)$ be a normal matrix and assume that $lambda$ is a given complex number that is not eigenvalue of matrix $A$. We present a method to calculate the distance norm (with respect to 2-norm) from $D$ to ...
متن کاملConstruction of matrices with prescribed singular values and eigenvalues
Two issues concerning the construction of square matrices with prescribed singular values and eigenvalues are addressed. First, a necessary and sufficient condition for the existence of an n × n complex matrix with n given nonnegative numbers as singular values and m(≤ n) given complex numbers to be m of the eigenvalues is determined. This extends the classical result of Weyl and Horn treating ...
متن کاملProperties of matrices with numerical ranges in a sector
Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...
متن کاملCommutative law for products of infinitely large isotropic random matrices.
Ensembles of isotropic random matrices are defined by the invariance of the probability measure under the left (and right) multiplication by an arbitrary unitary matrix. We show that the multiplication of large isotropic random matrices is spectrally commutative and self-averaging in the limit of infinite matrix size N→∞. The notion of spectral commutativity means that the eigenvalue density of...
متن کامل