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On the second real eigenvalue of nonegative and Z-matrices

✍ Scribed by Shmuel Friedland; Reinhard Nabben

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
564 KB
Volume
255
Category
Article
ISSN
0024-3795

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✦ Synopsis

We give bounds for the second real eigenvalue of nonegative matrices and Z-matrices. Furthermore, we establish upper bounds for the maximal spectral radii of principal submatrices of nonnegative matrices. Using these bounds, we prove that our inequality for the second real eigenvalue of the adjacency matrix of a connected regular graph improves a well-known bound for the second eigenvalue using Cheeger's inequality.

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