✦ LIBER ✦
Eigenvalues and Jordan canonical form of a successively rank-one updated complex matrix with applications to Google's PageRank problem
✍ Scribed by Gang Wu
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 153 KB
- Volume
- 216
- Category
- Article
- ISSN
- 0377-0427
No coin nor oath required. For personal study only.
✦ Synopsis
Let A be an n × n complex matrix with eigenvalues 1 , . . . , n counting algebraic multiplicities. Let X = [x 1 , . . . , x k ] be a rank-k matrix such that x 1 , . . . , x k are right eigenvectors of A corresponding to 1 , . . . , k for 1 k n, respectively, and V =[v 1 , . . . , v k ] ∈ C n×k be complex matrix. The eigenvalues and Jordan canonical form of the complex matrix A + k i=1 x i v H i are derived. The applications of our results to Google's PageRank problem are also discussed.