De Terán, Fernando and Lippert, Ross A and Nakatsukasa, Yuji and Noferini, Vanni (2014) Flandersʼ theorem for many matrices under commutativity assumptions. Linear Algebra and its Applications, 443. pp. 120-138. DOI https://doi.org/10.1016/j.laa.2013.11.026
De Terán, Fernando and Lippert, Ross A and Nakatsukasa, Yuji and Noferini, Vanni (2014) Flandersʼ theorem for many matrices under commutativity assumptions. Linear Algebra and its Applications, 443. pp. 120-138. DOI https://doi.org/10.1016/j.laa.2013.11.026
De Terán, Fernando and Lippert, Ross A and Nakatsukasa, Yuji and Noferini, Vanni (2014) Flandersʼ theorem for many matrices under commutativity assumptions. Linear Algebra and its Applications, 443. pp. 120-138. DOI https://doi.org/10.1016/j.laa.2013.11.026
Abstract
We analyze the relationship between the Jordan canonical form of products, in different orders, of k square matrices <sup>A1</sup>,.,<sup>Ak</sup>. Our results extend some classical results by H. Flanders. Motivated by a generalization of Fiedler matrices, we study permuted products of <sup>A1</sup>,.,<sup>Ak</sup> under the assumption that the graph of non-commutativity relations of <sup>A1</sup>,.,<sup>Ak</sup> is a forest. Under this condition, we show that the Jordan structure of all nonzero eigenvalues is the same for all permuted products. For the eigenvalue zero, we obtain an upper bound on the difference between the sizes of Jordan blocks for any two permuted products, and we show that this bound is attainable. For k=3 we show that, moreover, the bound is exhaustive. © 2013 Elsevier Inc.
Item Type: | Article |
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Uncontrolled Keywords: | Eigenvalue; Jordan canonical form; Segre characteristic; Product of matrices; Permuted products; Flanders' theorem; Forest; Cut-flip |
Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 20 Oct 2015 13:21 |
Last Modified: | 18 Jun 2025 06:46 |
URI: | http://repository.essex.ac.uk/id/eprint/15322 |