Skip to main content
SpringerLink
Log in

Generalized Jordan matrix of a linear operator

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

For any linear operator defined over an arbitrary field k, there is a basis in which this matrix is a generalized Jordan matrix (of the second kind) with elements in the field k. For any linear operator, such a matrix is defined uniquely up to permutation of diagonal blocks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. M. Postnikov, Linear Algebra and Differential Geometry, Lectures in Geometry; Semester 2 (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  2. A. I. Mal’tsev [Mal’cev], Foundations of Linear Algebra (Nauka, Moscow, 1975) [in Russian].

    Google Scholar 

  3. N. Bourbaki, Elements de mathématiques. Première partie: Les structures fondamentales de l’analyse. Livre II: Algèbre. Ch. 7–9 (Hermann et Cie, Paris, 1952 (Ch. 7); Hermann, Paris, 1958, 1959 (Ch. 8–9); “Nauka”, Moscow, 1966).

    Google Scholar 

  4. S. Al Fakir, Algèbre et théorie des nombres: cryptographie, primalité (Ellipses, Paris, 2003).

    MATH  Google Scholar 

  5. M. Artin, Algebra (Prentice Hall, New Jersey, 1991).

    Google Scholar 

  6. A. I. Kostrikin and Yu. I. Manin, Linear Algebra and Geometry, 2nd ed. (Nauka, Moscow, 1986; Gordon and Breach Science Publishers, New York, 1989).

    Google Scholar 

  7. S. G. Dalalyan, “Generalized Jordan normal form of a matrix with separable irreducible divisors of the characteristic polynomial,” Vestnik Ross.-Armyan. Gos. Usiv., Fiz.-Mat. Estest. Nauki 1, 7–14 (2005) [in Russian].

    Google Scholar 

  8. I. R. Shafarevich, Basic Notions of Algebra (Reg. Khaot. Dinam., Moscow, 2001; Springer-Verlag, Berlin, 2005).

    Google Scholar 

  9. S. Lang, Algebra (Addison-Wesley Publishing Co., Reading, Mass., 1965; Mir, Moscow, 1968).

    MATH  Google Scholar 

  10. N. Bourbaki, Algebra, II, Chaps. 4–7 (Springer-Verlag, Berlin, 1990; Nauka, Moscow, 1965; Hermann, Paris, 1959 (Chaps. 4–5), Hermann et Cie, Paris, 1952 (Chaps. 6–7)).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Erevan State University, USA

    S. G. Dalalyan

Authors
  1. S. G. Dalalyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. G. Dalalyan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dalalyan, S.G. Generalized Jordan matrix of a linear operator. Math Notes 82, 25–32 (2007). https://doi.org/10.1134/S0001434607070048

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434607070048

Key words

Search

Navigation