Skip to main content
Log in

Maximum Singular Value of Matrix and its Economic Interpretation

Cybernetics and Systems Analysis Aims and scope

Abstract

We prove that the maximum singular value of the matrix and the corresponding singular vectors are the optimal solution for a special quadratic optimization problem. We consider the economic interpretation of the optimal solution for the linear model of production and for the productive Leontief model. We relate the optimal solution to the Frobenius number and vectors and compare the Frobenius numbers and maximum singular values for Leontief inverse matrix in the 15-sectoral balance of Ukraine for 2003–2009.

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.

Institutional subscriptions

References

  1. S. A. Ashmanov, Introduction to Mathematical Economics [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  2. O. I. Ponomarenko, M. O. Perestyuk, and V. M. Burym, Modern Economic Analysis. Pt. 2: Macroeconomics [in Russian], Vyshcha Shkola, Kyiv (2004).

    Google Scholar 

  3. P. I. Stetsyuk, “The quadratic problem for the maximum singular number,” in: Trans. Intern. Sci. Conf. “The Issues of Calculation Optimization ISCOPT-XL” devoted to the 90th birthday anniversary of Acad. V. M. Glushkov, Ukraine, Crimea, Katsiveli, Sept. 30–Oct. 4, 2013, V. M. Glushkov Inst. of Cybernetics, NAS of Ukraine, 2013.

  4. P. I. Stetsyuk and L. B. Koshlai, “Optimal normalized structure of demand and value added in a productive Leontief model,” Cybern. Syst. Analysis, 46, No. 5, 729–737 (2010).

    Article  MathSciNet  Google Scholar 

  5. P. I. Stetsyuk and A. V. Bondarenko, “Spectral properties of the Leontief model,” Teoriya Optim. Reshenii, No. 10, 84–90 (2011).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. I. Stetsyuk.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2014, pp. 51–57.

The study was partially supported by the grant SNSF-SCOPES Project Nr. 127962 (Valorisation Grant).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stetsyuk, P.I., Emmenegger, JF. Maximum Singular Value of Matrix and its Economic Interpretation. Cybern Syst Anal 50, 368–373 (2014). https://doi.org/10.1007/s10559-014-9625-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-014-9625-5

Keywords

Navigation