# Testing Simultaneous Diagonalizability

arXiv: https://arxiv.org/abs/2101.07776 · HTML: https://mlsanity.com/paper/2101.07776/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2021.

## Built on by (most cited first, 1 of 1)

- [Hypothesis testing on invariant subspaces of non-diagonalizable matrices with applications to network statistics](https://mlsanity.com/paper/2303.18233/) (2023)

## Abstract (arXiv)

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.