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Maximum Singular Value of Matrix and its Economic Interpretation

Cybernetics and Systems Analysis Aims and scope


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.

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Correspondence to P. I. Stetsyuk.

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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).

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Stetsyuk, P.I., Emmenegger, JF. Maximum Singular Value of Matrix and its Economic Interpretation. Cybern Syst Anal 50, 368–373 (2014).

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