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  4. Theorems of Perron-Frobenius type for matrices without sign restrictions
 
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Theorems of Perron-Frobenius type for matrices without sign restrictions

Publikationstyp
Journal Article
Date Issued
1997-11-15
Sprache
English
Author(s)
Rump, Siegfried M.  orcid-logo
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/9392
Journal
Linear algebra and its applications  
Volume
266
Issue
1-3
Start Page
1
End Page
42
Citation
Linear Algebra and Its Applications 266 (1-3): 1-42 (1997-11-15)
Publisher DOI
10.1016/S0024-3795(96)00522-8
Scopus ID
2-s2.0-21944435802
Publisher
American Elsevier Publ.
The paper attempts to solve a problem which was called a "challenge for the future" in Linear Algebra Appl. We define and investigate a new quantity for real matrices, the sign-real spectral radius, and derive various characterizations, bounds, and properties of it. In certain aspects our quantity shows similar behavior to the Perron root of a nonnegative matrix. It is shown that our quantity also has intimate connections to the componentwise distance to the nearest singular matrix. Relations to the Perron root of the (entrywise) absolute value of the matrix and to the μ-number are given as well.
DDC Class
004: Informatik
510: Mathematik
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