| Title:
|
The real symmetric matrices of odd order with a P-set of maximum size (English) |
| Author:
|
Du, Zhibin |
| Author:
|
da Fonseca, Carlos M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
1007-1026 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose that $A$ is a real symmetric matrix of order $n$. Denote by $m_A(0)$ the nullity of $A$. For a nonempty subset $\alpha $ of $\{1,2,\ldots ,n\}$, let $A(\alpha )$ be the principal submatrix of $A$ obtained from $A$ by deleting the rows and columns indexed by $\alpha $. When $m_{A(\alpha )}(0)=m_{A}(0)+|\alpha |$, we call $\alpha $ a P-set of $A$. It is known that every P-set of $A$ contains at most $\lfloor {n}/{2} \rfloor $ elements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As a first step to the full characterization of these graphs of odd order, we establish some conditions for such graphs $G$ under which there is a real symmetric matrix $A$ whose graph is $G$ and contains a P-set of size ${(n-1)}/{2}$. (English) |
| Keyword:
|
real symmetric matrix |
| Keyword:
|
graph |
| Keyword:
|
multiplicity of eigenvalues |
| Keyword:
|
P-set |
| Keyword:
|
P-vertices |
| MSC:
|
05C50 |
| MSC:
|
15A18 |
| idZBL:
|
Zbl 06644047 |
| idMR:
|
MR3556881 |
| DOI:
|
10.1007/s10587-016-0306-6 |
| . |
| Date available:
|
2016-10-01T15:44:49Z |
| Last updated:
|
2023-10-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145885 |
| . |
| Reference:
|
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