Testing Simultaneous Diagonalizability

This paper proposes novel methods to test for simultaneous diagonalization of possibly asymmetric matrices. Motivated by various applications, a two-sample test as well as a generalization for multiple matrices are proposed. A partial version of the test is also studied to check whether a partial se...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Authors: Xu, Yuchen, Düker, Marie-Christine, Matteson, David S
Format: Article
Language:English
Subjects:
Algorithms
Eigenvectors
Markov chains
Online Access:Get full text
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Summary:This paper proposes novel methods to test for simultaneous diagonalization of possibly asymmetric matrices. Motivated by various applications, a two-sample test as well as a generalization for multiple matrices are proposed. A partial version of the test is also studied to check whether a partial set of eigenvectors is shared across samples. Additionally, a novel algorithm for the considered testing methods is introduced. Simulation studies demonstrate favorable performance for all designs. Finally, the theoretical results are utilized to decouple vector autoregression models into multiple univariate time series, and to test for the same stationary distribution in recurrent Markov chains. These applications are demonstrated using macroeconomic indices of 8 countries and streamflow data, respectively.
ISSN:2331-8422
DOI:10.48550/arxiv.2101.07776