The real symmetric matrices of odd order with a P-set of maximum size

Title:

The real symmetric matrices of odd order with a P-set of maximum size

Creator:

Du, Zhibin and da Fonseca, Carlos M

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:bb21034f-1402-4171-aa62-5d31ac6952c8
uuid:bb21034f-1402-4171-aa62-5d31ac6952c8
issn:0011-4642

Subject:

matematika, mathematics, real symmetric matrix, graph, multiplicity of eigenvalues, P-set, P-vertices, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Suppose that A is a real symmetric matrix of order n. Denote by m_{A}(0) the nullity of A. For a nonempty subset α of {1, 2,..., n}, let A(α) be the principal submatrix of A obtained from A by deleting the rows and columns indexed by α. When m_{A(\alpha )}(0) = m_{A}(0)+|α|, we call α a P-set of A. It is known that every P-set of A contains at most \left \lfloor n/2 \right \rfloorelements. 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., Zhibin Du, Carlos M. da Fonseca., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1007-1026

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:3

Harvested from:

CDK

Metadata only:

false