The codimension of degenerate pencils |
| |
| Authors: | Shmuel Friedland Barry Simon |
| |
| Affiliation: | Institute of Mathematics The Hebrew University Jerusalem, Israel;Mathematics Research Center University of Wisconsin Madison, Wisconsin USA;Department of Mathematics California Institute of Technology, Pasadena, California USA;Department of Mathematics and Physics Princeton University, Princeton, New Jersey USA |
| |
| Abstract: | Let dn[dn(r)] denote the codimension of the set of pairs of n×n Hermitian [really symmetric] matrices (A, B) for which det(λI?A?xB)=p(λ,x) is a reducible polynomial. We prove that dn(r)?n?1, dn?n?1 (n odd), dn?n (n even). We conjecture that the equality holds in all three inequalities. We prove this conjecture for n=2,3. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
