Article ID Journal Published Year Pages File Type
4642334 Journal of Computational and Applied Mathematics 2008 7 Pages PDF
Abstract

Let A   be an n×nn×n complex matrix with eigenvalues λ1,…,λnλ1,…,λn counting algebraic multiplicities. Let X=[x1,…,xk]X=[x1,…,xk] be a rank-k   matrix such that x1,…,xkx1,…,xk are right eigenvectors of A   corresponding to λ1,…,λkλ1,…,λk for 1⩽k⩽n1⩽k⩽n, respectively, and V=[v1,…,vk]∈Cn×kV=[v1,…,vk]∈Cn×k be complex matrix. The eigenvalues and Jordan canonical form of the complex matrix A+∑i=1kxiviH are derived. The applications of our results to Google's PageRank problem are also discussed.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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