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Flandersʼ theorem for many matrices under commutativity assumptions

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. ISSN 0024-3795

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Abstract

We analyze the relationship between the Jordan canonical form of products, in different orders, of k square matrices A1,.,Ak. Our results extend some classical results by H. Flanders. Motivated by a generalization of Fiedler matrices, we study permuted products of A1,.,Ak under the assumption that the graph of non-commutativity relations of A1,.,Ak 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
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 > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 20 Oct 2015 13:21
Last Modified: 15 Jan 2022 00:46
URI: http://repository.essex.ac.uk/id/eprint/15322

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