Skip to main content
SpringerLink
Log in

Real Orthogonal Projections as Quantum Logic

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In this paper, we study linear operators on real and complex Euclidean spaces which are real-orthogonal projections. It is a generalization of such standard (complex) orthogonal projections for which only the real part of scalar product vanishes. We can compare some partial order properties of the orthogonal and of the R-orthogonal projections. We prove that the set of all R-orthogonal projections in finite-dimensional complex space is a quantum logic.

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

Notes

  1. See https://en.wikipedia.org/wiki/Semiorthogonal_matrix.

References

  1. Ptak, P., Pulmannova, S.: Orthomodular structures as quantum logics. Kluver Acad. Publ. 44, 212 (1991)

    MATH  MathSciNet  Google Scholar 

  2. Matvejchuk, M.: Unitary self-adjoint logics of projections. Int. J. Theor. Phys. 37 (1), 103–107 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Matvejchuk, M.: Probability measures on conjugation logics. Positivity 1(3), 539–545 (2015). doi:10.1007/s11117-014-0314-4

    Article  MATH  MathSciNet  Google Scholar 

  4. Ando, T.: Projections in Krein spaces. Linear Algebra Appl. 12, 2346–2358 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Matvejchuk, M.: Gleason’s theorem in W*J-algebras in space with indefinite metric. Int. J. Theor. Phys. 38(8), 2065–2093 (1999). doi:10.1023/A:1026661904610

    Article  MATH  MathSciNet  Google Scholar 

  6. Matvejchuk, M.: Idempotents in a space with conjugation. Linear Algebra Appl. 438(1), 71–79 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  7. Groß, J., Trenkler, G., Troschke, S.: On semi-orthogonality and a special class of matrices. Linear Algebra Appl. 289, 169–182 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Matvejchuk, M., Widdows, D.: Real-orthogonal projections as quantum pseudo-logic. Lect. Notes Comput. Sci. 9535, 275–283 (2016). doi:10.1007/978-3-319-28675-4_21

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan National Research Tehnical University, ul. Karla Marksa, 10, Kazan, 420111, Russia

    Marjan Matvejchuk

Authors
  1. Marjan Matvejchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marjan Matvejchuk.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Matvejchuk, M. Real Orthogonal Projections as Quantum Logic. Int J Theor Phys 56, 3941–3952 (2017). https://doi.org/10.1007/s10773-017-3387-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-017-3387-6

Keywords

Search

Navigation