Name
Title | ||
|---|---|---|
A Systematic Analysis on Analyticity of Semisimple Eigenvalues of Matrix-Valued Functions. |
Abstract | ||
|---|---|---|
In this paper we study the existence of analytic eigenvalue functions of an analytic matrix-valued function L(lambda,rho). Instead of proposing sufficient conditions for each individual case as in the literature, we propose a systematic scheme to discuss the existence of analytic eigenvalue functions of L(lambda,rho) when lambda(0) is a semisimple eigenvalue of L(lambda, 0). We show that lambda(rho) = lambda(0)+rho mu(rho) is an eigenvalue of L(lambda,rho) if and only if mu(rho) is an eigenvalue of another analytic matrix-valued function P(mu,rho) which is constructed based on the first order (partial) derivatives of L(lambda,rho) at (lambda(0), 0). Based on this result, a systematic scheme is proposed to check whether there exist analytic eigenvalue functions of L(lambda,rho). This systematic scheme covers existing sufficient conditions in the literature, and can lead to much more general conditions. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/15M1053050 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
analytic eigenvalue function,semisimple eigenvalue,matrix-valued function | Combinatorics,Mathematical analysis,Matrix (mathematics),First order,Pure mathematics,Eigenvalues and eigenvectors,Mathematics,Lambda | Journal |
Volume | Issue | ISSN |
37 | 4 | 0895-4798 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jiang Qian | 1 | 7 | 2.66 |
| Delin Chu | 2 | 24 | 2.72 |
| Roger C. E. Tan | 3 | 102 | 19.13 |