Krylov Subspaces

Jonathan S. Golan ()
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Jonathan S. Golan: University of Haifa, Dept. of Mathematics

Chapter 13 in The Linear Algebra a Beginning Graduate Student Ought to Know, 2012, pp 297-316 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-007-2636-9_13

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DOI: 10.1007/978-94-007-2636-9_13

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