On ideal matrices whose entries are the generalized $ k- $Horadam numbers
Ideal matrices, which generalize circulant and $ r- $circulant matrices, play a key role in Ajtai's construction of collision-resistant hash functions. In this paper, we study ideal matrices whose entries are the generalized $ k- $Horadam numbers, which represent a generalization of second-orde...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-02-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025093 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850264503778803712 |
|---|---|
| author | Man Chen Huaifeng Chen |
| author_facet | Man Chen Huaifeng Chen |
| author_sort | Man Chen |
| collection | DOAJ |
| description | Ideal matrices, which generalize circulant and $ r- $circulant matrices, play a key role in Ajtai's construction of collision-resistant hash functions. In this paper, we study ideal matrices whose entries are the generalized $ k- $Horadam numbers, which represent a generalization of second-order sequences and include many well-known sequences such as Fibonacci, Lucas, and Pell numbers as special cases. We derive two explicit formulas for calculating the eigenvalues and determinants of these matrices. Additionally, we obtain upper bounds for the spectral norm and the Frobenius norm of ideal matrices with generalized $ k- $Horadam number entries. These results not only extend existing findings on ideal matrices but also highlight the versatility and applicability of generalized $ k- $Horadam numbers in matrix theory and related fields. |
| format | Article |
| id | doaj-art-2159b5e2ed4a450ba0ea00e60787fbc2 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-2159b5e2ed4a450ba0ea00e60787fbc22025-08-20T01:54:41ZengAIMS PressAIMS Mathematics2473-69882025-02-011021981199710.3934/math.2025093On ideal matrices whose entries are the generalized $ k- $Horadam numbersMan Chen0Huaifeng Chen1The 6th Research Institute of China Electronics Corporation, Beijing 102209, ChinaThe 6th Research Institute of China Electronics Corporation, Beijing 102209, ChinaIdeal matrices, which generalize circulant and $ r- $circulant matrices, play a key role in Ajtai's construction of collision-resistant hash functions. In this paper, we study ideal matrices whose entries are the generalized $ k- $Horadam numbers, which represent a generalization of second-order sequences and include many well-known sequences such as Fibonacci, Lucas, and Pell numbers as special cases. We derive two explicit formulas for calculating the eigenvalues and determinants of these matrices. Additionally, we obtain upper bounds for the spectral norm and the Frobenius norm of ideal matrices with generalized $ k- $Horadam number entries. These results not only extend existing findings on ideal matrices but also highlight the versatility and applicability of generalized $ k- $Horadam numbers in matrix theory and related fields.https://www.aimspress.com/article/doi/10.3934/math.2025093ideal matrixgeneralized $ k- $horadam numbersspectral normseigenvalues |
| spellingShingle | Man Chen Huaifeng Chen On ideal matrices whose entries are the generalized $ k- $Horadam numbers AIMS Mathematics ideal matrix generalized $ k- $horadam numbers spectral norms eigenvalues |
| title | On ideal matrices whose entries are the generalized $ k- $Horadam numbers |
| title_full | On ideal matrices whose entries are the generalized $ k- $Horadam numbers |
| title_fullStr | On ideal matrices whose entries are the generalized $ k- $Horadam numbers |
| title_full_unstemmed | On ideal matrices whose entries are the generalized $ k- $Horadam numbers |
| title_short | On ideal matrices whose entries are the generalized $ k- $Horadam numbers |
| title_sort | on ideal matrices whose entries are the generalized k horadam numbers |
| topic | ideal matrix generalized $ k- $horadam numbers spectral norms eigenvalues |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025093 |
| work_keys_str_mv | AT manchen onidealmatriceswhoseentriesarethegeneralizedkhoradamnumbers AT huaifengchen onidealmatriceswhoseentriesarethegeneralizedkhoradamnumbers |