In this work we discover for the first time a strong relationship between Geršgorin theory and the geometric multiplicities of eigenvalues. In fact, if λ is an eigenvalue of an n × n matrix A with geometric multiplicity k, then λ is in at least k Geršgorin discs of A. Moreover, construct the matrix C by replacing, in every row, the (k − 1) smallest off-diagonal entries in absolute value by 0, then λ is in at least k Geršgorin discs of C. We also state and prove many new applications and consequences of these results as well as we update an improve some important existing ones.
| Identifer | oai:union.ndltd.org:GEORGIA/oai:scholarworks.gsu.edu:math_diss-1027 |
| Date | 11 August 2015 |
| Creators | Marsli, Rachid |
| Publisher | ScholarWorks @ Georgia State University |
| Source Sets | Georgia State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Mathematics Dissertations |
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