On a spectral characterization of rank one matrices

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...

Rank-one Convexity Implies Quasiconvexity on Diagonal Matrices

The question of whether such a result holds was raised inTartar’s seminal paper [T1], where he proved estimate (1.3) under the stronger condition that ∂2uj and ∂1vj are bounded in Lloc. In this case, he even showed that the Young measure generated by the pair (uj, vj) (see below for definitions) is a tensor product, and he gave an example that this need no longer be the case if only (1.2) holds...

Bending Flows for Sums of Rank One 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.

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...