Skip to main content
Log in

Simultaneous reduction to block triangular form and theorems on pairs of complex idempotents

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

It is shown that the properties of idempotents found in recent journal publications can be justified in an easier way if a classical theorem concerning the simultaneous reduction of a pair of complex idempotents to block triangular form is used.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. H. F. Blichfeldt, Finite Collineation Groups (Univ. Chicago Press, Chicago, 1917).

    Google Scholar 

  2. Kh. D. Ikramov, “On Simultaneous Reduction of a Pair of Oblique Projectors to Block Triangular Form,” Zh. Vychisl. Mat. Mat. Fiz. 38, 181–182 (1998) [Comput. Math. Math. Phys. 38, 173–174 (1998)].

    MathSciNet  Google Scholar 

  3. S. Roch and B. Silbermann, “Algebras Generated by Idempotents and the Symbol Calculus for Singular Integral Operators,” Integral Equations Operator Theory 11, 385–419.

  4. I. Gohberg and N. Krupnik, “Extension Theorems for Invertibility Symbols in Banach Algebras,” Integral Equations Operator Theory 15, 991–1010 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  5. I. Gohberg and N. Krupnik, “Extension Theorems for Fredholm and Invertibility Symbols,” Integral Equations Operator Theory 16, 514–529 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. Böttcher and I. M. Spitkovsky, “A Gentle Guide to the Basics of Two Projections Theory,” Linear Algebra Appl. 432, 1412–1459 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Gross and G. Trenkler, “Nonsingularity of the Difference of Two Oblique Projectors,” SIAM J. Matrix Anal. Appl. 21, 390–395 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  8. K. Zuo, “Nonsingularity of the Difference and the Sum of Two Idempotent Matrices,” Linear Algebra Appl. 433, 476–482 (2010).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kh. D. Ikramov.

Additional information

Published in Russian in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 6, pp. 979–982.

The article was translated by the author.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ikramov, K.D. Simultaneous reduction to block triangular form and theorems on pairs of complex idempotents. Comput. Math. and Math. Phys. 51, 915–918 (2011). https://doi.org/10.1134/S0965542511060091

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542511060091

Keywords

Navigation