Skip to main content
SpringerLink
Log in

On building matrices in the theory of least squares method

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We construct samples of real matrices with number of rows greater than the number of columns and satisfying four requirements: the squares of the rows equal one, the squares of the columns equal each other, the columns are pairwise orthogonal, the sum of the components of each column is zero, except for two cases. In the first case, the number of rows is odd and the number of columns is one. In the second case, the number of rows is odd and the number of columns is two less than the number of rows. It is proved that in these cases, there are no matrices satisfying the four specified requirements. The place of matrices satisfying the four specified requirements is shown in the theory of errors in measuring systems such as GPS.

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. Legendre, A. M. Nouvelles methode pour la determination des orbites des cometes (Firmin Didot, Paris, 1805), 72–80.

    Google Scholar 

  2. Kolmogorov, A. N., Petrov, A. A., Smirnov, Yu. M. “A formula of Gauss in the theory of least quadrature”, Izv. Akad. Nauk SSSR Ser. Mat. 11, 561–566 (1947). [in Russian]

    MATH  Google Scholar 

  3. Mal’tsev, A. I. “Bemerkung zu der Arbeit von A. N. Kolmogorov, A. A. Petrov und Yu. M. Smirnov “Eine Formel von Gauss aus der Theorie der kleinsten Quadrate””, Izv. Akad. Nauk SSSR Ser. Mat. 11, 567–568 (1947). [in Russian]

    MATH  Google Scholar 

  4. Barabanov, O. O., Barabanova, L. P. Mathematical problems of long-distance navigation (Fizmatlit, Moscow, 2007). [in Russian]

    MATH  Google Scholar 

  5. Barabanova, L. P. “On minimisation of GNSS geometric factors”, J. Comput. Syst. Sci. Int. 49, No. 2, 310–317 (2010).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kovrov State Technological Academy named after V.A. Degtyarev, 19 Mayakovskogo str., Kovrov, 601910, Russia

    O. O. Barabanov & L. P. Barabanova

Authors
  1. O. O. Barabanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. P. Barabanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to O. O. Barabanov or L. P. Barabanova.

Additional information

Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 4, pp. 27–35.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barabanov, O.O., Barabanova, L.P. On building matrices in the theory of least squares method. Russ Math. 63, 23–30 (2019). https://doi.org/10.3103/S1066369X19040030

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X19040030

Key words

Search

Navigation