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Abstract

Krylov subspaces are studied theoretically and as the foundation of Krylov iterative algorithms for approximating the solutions to systems of linear equations. The Rational Decomposition Theorem for nilpotent endomorphisms is proven and used to define the Jordan canonical form. Every square matrix over an algebraically-closed field is shown to be a product of two symmetric matrices and to be similar to its transpose.

Keywords

Finite Field Characteristic Polynomial Canonical Basis Krylov Subspace Minimal Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Dept. of MathematicsUniversity of HaifaHaifaIsrael

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