Eigenvalues and Jordan canonical form of a successively rank-one updated complex matrix with applications to Google's PageRank problem
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摘要
Let A be an n×n complex matrix with eigenvalues λ1,…,λn counting algebraic multiplicities. Let X=[x1,…,xk] be a rank-k matrix such that x1,…,xk are right eigenvectors of A corresponding to λ1,…,λk for 1⩽k⩽n, respectively, and V=[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.
论文关键词:65F15,65F10,65C40,Pagerank,Google matrix,Jordan canonical form,Successively rank-one updated matrix,Generalized Google matrix
论文评审过程:Received 13 November 2006, Revised 8 April 2007, Available online 24 May 2007.
论文官网地址:https://doi.org/10.1016/j.cam.2007.05.015