For a -matrix =+–, diagonal, Hermitian, is a candidate for being a closest normal matrix to . The additional, second-order optimality condition is reformu... L. LASZLO - 《Bit Numerical Mathematics》 被引量: 1发表: 2003年 On Eigenvalue Optimization In that framework we discuss first- ...
Consider a matrix function f defined for Hermitian matrices. The purpose of this paper is two-fold. We derive new results for the absolute structured condition number of the matrix function and we derive new bounds for the perturbation ||f(A+E)-f(A)|| expressed in terms of eigenvalues of...
Using the existence condition of Hermitian matrix P=P∗ for a complex Lyapunov inequality, we proved that a fractional-order interval linear system is robust stable if and only if there exist Acknowledgment The reviewers’ comments, which have improved the quality of this paper, are greatly ...
linear matrix equationsbackward perturbation boundThis paper deals with the normwise perturbation theory for linear (Hermitian) matrix equations. The definition of condition number for the linear (Hermitian) matrix equations is presented. The lower and upper bounds for the condition number are derived....
We introduce the notion ofpseudo-Hermiticityand show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all thePT-symmetric... A Mostafazadeh - 《Journal of Mathematical Physics》 被引量: 1066发表: 2002年 On the Digraph of a Unitary Matrix We give a necessary...
We define in the space of n x m matrices of rank n, n <= m, the condition Riemannian structure as follows: For a given matrix A the tangent space at A is equipped with the Hermitian inner product obtained by multiplying the usual Frobenius inner product by the inverse of the square of...
(optional) equation of the form conjugate=true or false; specifies if the result in the 2-norm case uses the Hermitian transpose Description • The ConditionNumber(A) function computes the scalar quantity equal to the condition number of A as NormA,∞NormMatrixInverse...
Unitarity is a consistency condition for any quantum theory. Formally, a q...C.-S. Chu, J. Lukierski, and W. J. Zakrzewski, "Hermitian analyticity, IR/UV mix- ing and unitarity of noncommutative field theories," Nucl. Phys... CA Chongsun,LB Jerzy,JZA Wojtek 被引量: 61发表: 2002...
where H is the Hermitian matrix operator and fred≔THf={flb+λy−1flt+λy−12flfrb+λy−1frt+λy−12frfb+λy−1ft+λy−12fi}={fLfRfO}. Since the internal nodal forces are zero, fi=0, and due to the equilibrium conditions on the bottom edge of the segment fb+λy...
In other words, the existence of a quadratic common Lyapunov function for the family of linear systems (2) guarantees global uniform exponential stability of (1). are positive. Lemma 4 All leading principal minors of a Hermitian matrix are real. A Hermitian matrix H is positive de nite (i....