Eigenstructure of rank one updated matrices

Eigenvalues of rank-one updated matrices with some applications

We prove a spectral perturbation theorem for rank-one updated matrices of special structure. Two applications of the result are given to illustrate the usefulness of the theorem. One is for the spectrum of the Google matrix and the other is for the algebraic simplicity of the maximal eigenvalue of a positive matrix. c © 2007 Elsevier Ltd. All rights reserved.

On higher rank numerical hulls of normal matrices

‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...

Bending Flows for Sums of Rank One Matrices

Rank-one LMI approach to robust stability of polynomial matrices

Necessary and sufficient conditions are formulated for checking robust stability of an uncertain polynomial matrix. Various stability regions and uncertainty models are handled in a unified way. The conditions, stemming from a general optimization methodology similar to the one used in /i-analysis, are expressed as a rank-one LMI, a non-convex problem frequently arising in robust control. Conve...

Eigenstructure of Order-One-Quasiseparable Matrices. Three-term and Two-term Recurrence Relations

This paper presents explicit formulas and algorithms to compute the eigenvalues and eigenvectors of order-one-quasiseparable matrices. Various recursive relations for characteristic polynomials of their principal submatrices are derived. The cost of evaluating the characteristic polynomial of an N × N matrix and its derivative is only O(N). This leads immediately to several versions of a fast q...