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Equilibrium, Stability and GrowthA Multi-Sectoral Analysis$
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Michio Morishima

Print publication date: 1963

Print ISBN-13: 9780198281450

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198281455.001.0001

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(p.195) Appendix Generalizations of the Perron–Frobenius Theorems for Non‐Negative Square Matrices

(p.195) Appendix Generalizations of the Perron–Frobenius Theorems for Non‐Negative Square Matrices

Equilibrium, Stability and Growth

Michio Morishima

Oxford University Press

The Appendix generalizes the classical theorems on non‐negative square matrices to systems of non‐linear and homogeneous functions. Some of these results are repeatedly used in the text of the book, and all of them are of great importance to workers in the field of multisectoral analysis. The different sections of the Appendix address non‐linear eigenvector problems, balanced growth, stability, and the non‐linear resolvent problem. Other mathematical theorems and concepts that are not familiar to economists are explained in footnotes of the chapters in which they are used for the first time.

Keywords:   balanced growth, generalization, multisectoral analysis, non‐linear eigenvectors, non‐linear resolvence, non‐negative matrices, Perron–Frobenius Theorems, stability

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