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Paper Abstract and Keywords
Presentation 2025-03-02 11:00
Joint Diagonalization Based on Equivalence Classes of Orthogonal Matrices by Signed Permutations and Weighted Averaging in the Cayley Transform Domain
Akira Tanaka, Takafumi Edo (Hokkaido Univ.) EA2024-85 SIP2024-120 SP2024-26
Abstract (in Japanese) (See Japanese page) 
(in English) In our previous work, we proposed a novel closed-form solution for joint diagonalization of real non-negative symmetric matrices which are not jointly diagonalizable strictly. The key idea of this solution is adopting a weighted average of orthogonal matrices, that form part of the closed-form solution, in the Cayley transform domain. In this method, a certain pre-processing for the orthogonal matrices is required in order for the weighted averaging works properly. However, we have to exclude some of the orthogonal matrices for which the pre-precessing does not work properly.
In this paper, we construct a novel pre-processing algorithm based on the recent knowledge on a signed permutation of an orthogonal matrix and its Cayley transform.
We also verify its validity through numerical examples.
Keyword (in Japanese) (See Japanese page) 
(in English) joint diagonalization / Cayley transform / orthogonal matrices / signed permutations / equivalence class / / /  
Reference Info. IEICE Tech. Rep., vol. 124, no. 390, SIP2024-120, pp. 52-57, March 2025.
Paper # SIP2024-120 
Date of Issue 2025-02-23 (EA, SIP, SP) 
ISSN Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF EA2024-85 SIP2024-120 SP2024-26

Conference Information
Committee EA SIP SP IPSJ-SLP  
Conference Date 2025-03-02 - 2025-03-04 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To SIP 
Conference Code 2025-03-EA-SIP-SP-SLP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Joint Diagonalization Based on Equivalence Classes of Orthogonal Matrices by Signed Permutations and Weighted Averaging in the Cayley Transform Domain 
Sub Title (in English)  
Keyword(1) joint diagonalization  
Keyword(2) Cayley transform  
Keyword(3) orthogonal matrices  
Keyword(4) signed permutations  
Keyword(5) equivalence class  
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Keyword(7)  
Keyword(8)  
1st Author's Name Akira Tanaka  
1st Author's Affiliation Hokkaido University (Hokkaido Univ.)
2nd Author's Name Takafumi Edo  
2nd Author's Affiliation Hokkaido University (Hokkaido Univ.)
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Speaker Author-1 
Date Time 2025-03-02 11:00:00 
Presentation Time 20 minutes 
Registration for SIP 
Paper # EA2024-85, SIP2024-120, SP2024-26 
Volume (vol) vol.124 
Number (no) no.389(EA), no.390(SIP), no.391(SP) 
Page pp.52-57 
#Pages 6 
Date of Issue 2025-02-23 (EA, SIP, SP) 

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