2009•Journal of Shandong UniversityRequires access

Lower bounds for the rank and estimation for eigenvalues

Junliang Wu

Abstract

Lower bounds for the rank and the estimation for eigenvalues of matrices are discussed.Two lower bounds for the rank and estimation for the real part and imaginary part of eigenvalues are obtained.Also,we prove that all the eigenvalues of any complex matrix are located in one disk.Some numerical examples show the effectiveness of our results.

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Key concepts: Eigenvalues and eigenvectors, Rank (graph theory), Mathematics, Estimation, Matrix (chemical analysis), Combinatorics, Upper and lower bounds, Applied mathematics