Confluent Vandermonde matrix and related topics
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915461581504512 |
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| author | Li, Chi-Kwong Lin, Jephian C. -H. |
| author_facet | Li, Chi-Kwong Lin, Jephian C. -H. |
| contents | In this note, we explore the connections between the confluent Vandermonde matrix over an arbitrary field and several mathematical topics, including interpolation polynomials, Hasse derivatives, LU factorization, companion matrices and their Jordan forms, and the partial fraction decomposition. Using a unified approach based on polynomial evaluations and derivative computations at selected points, we provide accessible proofs that not only clarify key results but also offer insights for both experienced researchers and those new to the subject. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01474 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Confluent Vandermonde matrix and related topics Li, Chi-Kwong Lin, Jephian C. -H. Combinatorics 15A20, 15A21, 15A23, 33C45 In this note, we explore the connections between the confluent Vandermonde matrix over an arbitrary field and several mathematical topics, including interpolation polynomials, Hasse derivatives, LU factorization, companion matrices and their Jordan forms, and the partial fraction decomposition. Using a unified approach based on polynomial evaluations and derivative computations at selected points, we provide accessible proofs that not only clarify key results but also offer insights for both experienced researchers and those new to the subject. |
| title | Confluent Vandermonde matrix and related topics |
| topic | Combinatorics 15A20, 15A21, 15A23, 33C45 |
| url | https://arxiv.org/abs/2403.01474 |