Some applications of spectral theory of nonnegative matrices to input-output models

DOI10.1016/S0024-3795(01)00324-XzbMath0995.15017WikidataQ127840735 ScholiaQ127840735MaRDI QIDQ5954854

Lisheng Zeng

Publication date: 23 October 2002

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

reducibilitynonnegative matricesinput-output modelFrobenius normal form\(M\)-splittingbalanced growth solutionbasic characteristic subvectoriteration matrixpositive eigenvector

Mathematics Subject Classification ID

Multisectoral models in economics (91B66) Economic growth models (91B62) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Canonical forms, reductions, classification (15A21)

Related Items (6)

Parameter identification of a class of economical models ⋮ Effects of changes in outputs and in prices on the economic system: an input-output analysis using the spectral theory of nonnegative matrices ⋮ Conditions for some balances of economic system: an input-output analysis using the spectral theory of nonnegative matrices ⋮ Positive solutions of a discrete-time descriptor system ⋮ Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices ⋮ Looking for nonnegative solutions of a Leontief dynamic model.

Cites Work

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• The influence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties: a survey
• Theorems on M-splittings of a singular M-Matrix which depend on graph structure
• Convergence of nested classical iterative methods for linear systems
• Splittings ofM-operators: Irreducibility and the index of the iteration operator
• Conditions for the Existence of a Balance Growth Solution for the Leontief Dynamic Input-Output Model
• On Nonnegative Solutions of Matrix Equations
• A Note on M-Matrix Equations

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