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Krylov Subspaces

In: The Linear Algebra a Beginning Graduate Student Ought to Know

Author

Listed:
  • Jonathan S. Golan

    (University of Haifa, Dept. of Mathematics)

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.

Suggested Citation

  • Jonathan S. Golan, 2012. "Krylov Subspaces," Springer Books, in: The Linear Algebra a Beginning Graduate Student Ought to Know, edition 3, chapter 13, pages 297-316, Springer.
    • Handle: RePEc:spr:sprchp:978-94-007-2636-9_13
    DOI: 10.1007/978-94-007-2636-9_13
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