Generalizations of the Perron–Frobenius Theorems for Non‐Negative Square Matrices

Abstract

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.