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arXiv · 1506.08257

Eigenschemes and the Jordan canonical form

Hirotachi Abo·David Eklund·Thomas Kahle·Chris Peterson
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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.

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Hirotachi Abo, David Eklund, Thomas Kahle, Chris Peterson. 2015-06-27. Eigenschemes and the Jordan canonical form. https://doi.org/10.1016/j.laa.2015.12.030

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