Spectrum of a matrix

About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.

Computation of Eigenvalues

Abstract: This chapter deals with eigenvalues and eigenvectors of matrices. The material here is a sequel to Chapter 2 dealing with the solution of linear equations. Eigenvalues are very important since many engineering problems naturally lead to eigenvalue problems. When the size of a matrix is large special numerical methods are necessary for obtaining eigenvalues and eigenvectors.

Error estimate of eigenvalues of discrete linear Hamiltonian systems with small perturbation

Abstract: In this paper, eigenvalues of perturbed discrete linear Hamiltonian systems are considered. A new variational formula of eigenvalues is first established. Based on it, error estimates of eigenvalues of systems with small perturbation are given under certain non-singularity conditions. Small perturbations of the coefficient functions, the weight function and the coefficients of the boundary condition are all involved. As a direct consequence, continuous dependence of eigenvalues on boundary value problems is obtained under the non-singularity conditions. In addition, two examples are presented to illustrate the necessity of the non-singularity conditions and the complexity of the problem in the singularity case.

Median modal control of interval continuous-time plants

Abstract: In this paper we consider a system with interval state matrix. Control law ensures desired eigenvalues and relative uncertainty of the closed-loop system state matrix. An example is given.