Symmetric and skew-symmetric {0, ±1} - matrices with large determinants
We show that the existence of {±}-matrices having largest possible determinant is equivalent to the existence of certain tournament matrices. In particular, we prove a recent conjecture of Armario. We also show that large submatrices of conference matrices are determined by their spectrum.
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| Format: | Journal Article |
| Language: | English |
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2020
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| Online Access: | https://hdl.handle.net/10356/144977 |
| _version_ | 1826116497439719424 |
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| author | Greaves, Gary Suda, Sho |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Greaves, Gary Suda, Sho |
| author_sort | Greaves, Gary |
| collection | NTU |
| description | We show that the existence of {±}-matrices having largest possible determinant is equivalent to the existence of certain tournament matrices. In particular, we prove a recent conjecture of Armario. We also show that large submatrices of conference matrices are determined by their spectrum. |
| first_indexed | 2024-10-01T04:12:23Z |
| format | Journal Article |
| id | ntu-10356/144977 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:12:23Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1449772023-02-28T19:52:50Z Symmetric and skew-symmetric {0, ±1} - matrices with large determinants Greaves, Gary Suda, Sho School of Physical and Mathematical Sciences Mathematics - Combinatorics Mathematics - Combinatorics Science::Mathematics D‐optimal Design EW Matrix We show that the existence of {±}-matrices having largest possible determinant is equivalent to the existence of certain tournament matrices. In particular, we prove a recent conjecture of Armario. We also show that large submatrices of conference matrices are determined by their spectrum. Accepted version 2020-12-07T07:27:00Z 2020-12-07T07:27:00Z 2016 Journal Article Greaves, G., & Suda, S. (2017). Symmetric and Skew-Symmetric {0,±1}-Matrices with Large Determinants. Journal of Combinatorial Designs, 25(11), 507–522. doi:10.1002/jcd.21567 1063-8539 https://hdl.handle.net/10356/144977 10.1002/jcd.21567 11 25 507 522 en Journal of Combinatorial Designs This is the accepted version of the following article: Greaves, G., & Suda, S. (2017). Symmetric and Skew-Symmetric {0,±1}-Matrices with Large Determinants. Journal of Combinatorial Designs, 25(11), 507–522., which has been published in final form at 10.1002/jcd.21567. This article may be used for non-commercial purposes in accordance with the Wiley Self-Archiving Policy [https://authorservices.wiley.com/authorresources/Journal-Authors/licensing/self-archiving.html]. application/pdf |
| spellingShingle | Mathematics - Combinatorics Mathematics - Combinatorics Science::Mathematics D‐optimal Design EW Matrix Greaves, Gary Suda, Sho Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| title | Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| title_full | Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| title_fullStr | Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| title_full_unstemmed | Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| title_short | Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| title_sort | symmetric and skew symmetric 0 1 matrices with large determinants |
| topic | Mathematics - Combinatorics Mathematics - Combinatorics Science::Mathematics D‐optimal Design EW Matrix |
| url | https://hdl.handle.net/10356/144977 |
| work_keys_str_mv | AT greavesgary symmetricandskewsymmetric01matriceswithlargedeterminants AT sudasho symmetricandskewsymmetric01matriceswithlargedeterminants |