Event
01_1
| 제출번호(No.) | 0013 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Algebra (AL) |
| 영문제목 (Title(Eng.)) |
Completely positive matrix rank and its linear preservers |
| 저자(Author(s)) |
Seok-Zun Song1 Jeju National University1 |
| 초록본문(Abstract) | Let M_{mn}(R) denote the set of m by n matrices with entries in real numbers. We write M_{mn}(R_+ ) to denote the subset of M_{mn}(R), all of whose entries are nonnegative. Let S_{n}(R) denote the set of all n by n real symmetric matrices. A matrix A in S_{n}(R) is said to be completely positive if there is some matrix B in M_{n,k}(R_+) such that A=BB^t. The CP-rank of the matrix A is the smallest k such that A=BB^t for some B in M_{n,k}(R_+ ). In this talk, we shall investigate the linear operators on S_{n}(R) that preserve sets of matrices defined by the CP-rank. We classify those that preserve the CP-rank function, those that preserve the set of CP-rank-1 matrices, those that preserve the sets of CP-rank-1 matrices and the set of CP-rank-2 matrices, and those that strongly preserve the set of CP-rank-1 matrices. |
| 분류기호 (MSC number(s)) |
15A04, 15A86 |
| 키워드(Keyword(s)) | completely positive matrix, CP-rank, linear operator, (strong) linear preserver |
| 강연 형태 (Language of Session (Talk)) |
Korean |