Some New Inequalities on Geometric Multiplicities and Geršgorin Discs

Copyright c © 2014 Rachid Marsli and Frank J. Hall. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper the authors continue their work on geometric multiplic-ities and Geřsgorin discs done in a series of four recent papers. The new results involve principal submatrices, an upper bound on the absolute value of an eigenvalue, the rank of a matrix, non-real eigenvalues, and powers of matrices. Some consequences of the results and examples are provided. mathematics Subject Classification: 15A1