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.


Finite Field Characteristic Polynomial Canonical Basis Krylov Subspace Minimal Polynomial 
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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Dept. of MathematicsUniversity of HaifaHaifaIsrael

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