English

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 AA 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