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

Content Provider	Springer Nature Link
Author	Du, Zhibin Fonseca, Carlos M.
Copyright Year	2016
Abstract	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(α)(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 ⌊n/2⌋ 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.
Ending Page	1026
Page Count	20
Starting Page	1007
File Format	PDF
ISSN	00114642
e-ISSN	15729141
Journal	Czechoslovak Mathematical Journal
Issue Number	3
Volume Number	66
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-10-13
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Eigenvalues, singular values, and eigenvectors P-vertices Ordinary Differential Equations real symmetric matrix Analysis Convex and Discrete Geometry P-set multiplicity of eigenvalues Mathematics Graphs and linear algebra (matrices, eigenvalues, etc.) Mathematical Modeling and Industrial Mathematics graph
Content Type	Text
Resource Type	Article
Subject	Mathematics

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