Skip to main content
SpringerLink
Log in

Zur Matrizeninversion nach Gauss-Jordan

  • Originala Arbeiten
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Summary

The so-called ‘Gauss-Jordan’ procedure for inverting matrices has been described in many papers and is well known. The present paper gives an unusual approach to this method insofar as the inverse is obtained by repeated application of a certain non-similarity transformation to the original matrix. Of course this transformation is related to the Gauss elimination process, but formally has rather the character of an exchange of components in two vector spaces.

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

Literaturverzeichnis

  1. T. Banachiewicz,Méthode de résolution numérique des équations linéaires, du calcul des déterminants et des inverses et de réduction de formes quadratiques, Bull. internat. Acad. polon. Sci. [A]1938, 393–404.

  2. A. P. Ersov,Über eine Methode der Inversion von Matrizen (russisch), Doklady Akad. Nauk. SSSR.100, 209–211 (1955).

    Google Scholar 

  3. Jordan-Eggert,Handbuch der Vermessungslehre, Bd. 1, § 35, 8. Aufl. (Verlag Metazler, Stuttgart 1935), 630 S.

    Google Scholar 

  4. G. W. Petrie, III.,Matrix Inversion and Solution of Simultaneous Linear Algebraic Equations with the IBM 604 Electronic Calculating Punch, NBS, AMS,29, 107–111 (1953).

    Google Scholar 

  5. H. Rutishauser,Automatische Rechenplanfertigung bei programmgesteuerten Rechenmaschinen, Z. angew. Math. Phys.3, 312–313 (1952).

    Google Scholar 

  6. R. Zurmühl,Zur numerischen Auflösung linearer Gleichungssysteme nach dem Matrizenverfahren von Banachiewicz, Z. angew. Math. Mech.29, 76–84 (1949).

    Google Scholar 

  7. R. Zurmühl,Matrizen (Springer-Verlag, Berlin, Göttingen und Heidelberg 1950), 427 S.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für angewandte Mathematik der ETH, Zürich

    Heinz Rutishauser

Authors
  1. Heinz Rutishauser
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rutishauser, H. Zur Matrizeninversion nach Gauss-Jordan. Journal of Applied Mathematics and Physics (ZAMP) 10, 281–291 (1959). https://doi.org/10.1007/BF01600606

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01600606

Search

Navigation