On Determining the Eigenprojection and Components of a Matrix
Algebraic Geometry
2011-01-25 v2 Numerical Analysis
Rings and Algebras
Abstract
Matrix theory and its applications make wide use of the eigenprojections of square matrices. The present paper demonstrates that the eigenprojection of a matrix can be calculated with the use of any annihilating polynomial of A^u, where u >= ind A. This enables one to find the components and the minimal polynomial of A, as well as the Drazin inverse A^D.
Keywords
Cite
@article{arxiv.math/0508197,
title = {On Determining the Eigenprojection and Components of a Matrix},
author = {R. P. Agaev and P. Yu. Chebotarev},
journal= {arXiv preprint arXiv:math/0508197},
year = {2011}
}
Comments
9 pages. In this version, an inaccuracy in Proposition 2 is corrected and the result (explicit expressions for the eigenprojection and components of a matrix with known eigenvalues) is presented in a simpler form