论文标题
输入输出表和一些有缺陷矩阵的理论
Input-Output Tables and Some Theory of Defective Matrices
论文作者
论文摘要
生产网络理论的最新发展提供了有趣的应用程序和投入输出分析的复兴。最近的一些论文研究了通过输入输出网络的暂时负面冲击的传播。这种冲击传播的分析依赖于相关输入输出矩阵的特征分类。众所周知，只有可对角矩阵才能被特征组成。那些不可对角线的人称为缺陷矩阵。在本文中，我们使用其等级和特征值提供了任何正方形矩阵的对角线的必要条件。为了应用我们的结果，我们提供了1950年代印度的投入输出表的示例，这些表不可对角线，因此有缺陷。
Recent developments in the theory of production networks offer interesting applications and revival of input-output analysis. Some recent papers have studied the propagation of a temporary, negative shock through an input-output network. Such analyses of shock propagation relies on eigendecomposition of relevant input-output matrices. It is well known that only diagonalizable matrices can be eigendecomposed; those that are not diagonalizable, are known as defective matrices. In this paper, we provide necessary and sufficient conditions for diagonalizability of any square matrix using its rank and eigenvalues. To apply our results, we offer examples of input-output tables from India in the 1950s that were not diagonalizable and were hence, defective.
