Eigenschemes and the Jordan canonical form
Algebraic Geometry
2016-04-13 v3 Commutative Algebra
Abstract
We study the eigenscheme of a matrix which encodes information about the eigenvectors and generalized eigenvectors of a square matrix. The two main results in this paper are this decomposition encodes the numeric data of the Jordan canonical form of the matrix. We also describe how the eigenscheme can be interpreted as the zero locus of a global section of the tangent bundle on projective space. This interpretation allows one to see eigenvectors and generalized eigenvectors of matrices from an alternative viewpoint.
Keywords
Cite
@article{arxiv.1506.08257,
title = {Eigenschemes and the Jordan canonical form},
author = {Hirotachi Abo and David Eklund and Thomas Kahle and Chris Peterson},
journal= {arXiv preprint arXiv:1506.08257},
year = {2016}
}
Comments
23 pages; v3: minor corrections, final version as appeared in Linear Algebra Appl