Algebraic Aspects of combined matrices
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916499725221888 |
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| author | Acosta-Humánez, Primitivo B. Leonardo, Randy Santana, Máximo |
| author_facet | Acosta-Humánez, Primitivo B. Leonardo, Randy Santana, Máximo |
| contents | In this work, we present algebraic results concerning the combined matrices $\mathcal{C}(A)$, where the entries of $A$ belong to a number field $K$ and $A$ is a non-singular matrix. In other words, $A$ is a $n\times n$ matrix belonging to the General Linear Group over $K$, denoted by $\mathrm{GL}_n(K)$. We also analyze the case in which matrix $A$ belongs to algebraic subgroups of $\mathrm{GL}_n(K)$, such as the unimodular group, where $A^2$ is a $n\times n$ matrix belonging to the Special Linear Group, denoted by $\mathrm{SL}_n(K)$, triangular groups, diagonal groups, among others. In particular, we thouroughly examine the cases $n=2$ and $n=3$ for symmetric and non-symmetric matrices, providing explicit diagonalization of $\mathcal{C}(A)$, which includes characteristic polynomials with their eigenvalues and eigenfactors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_06848 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Algebraic Aspects of combined matrices Acosta-Humánez, Primitivo B. Leonardo, Randy Santana, Máximo Number Theory Combinatorics (Primary) 15A18 (Secondary) 05E99 In this work, we present algebraic results concerning the combined matrices $\mathcal{C}(A)$, where the entries of $A$ belong to a number field $K$ and $A$ is a non-singular matrix. In other words, $A$ is a $n\times n$ matrix belonging to the General Linear Group over $K$, denoted by $\mathrm{GL}_n(K)$. We also analyze the case in which matrix $A$ belongs to algebraic subgroups of $\mathrm{GL}_n(K)$, such as the unimodular group, where $A^2$ is a $n\times n$ matrix belonging to the Special Linear Group, denoted by $\mathrm{SL}_n(K)$, triangular groups, diagonal groups, among others. In particular, we thouroughly examine the cases $n=2$ and $n=3$ for symmetric and non-symmetric matrices, providing explicit diagonalization of $\mathcal{C}(A)$, which includes characteristic polynomials with their eigenvalues and eigenfactors. |
| title | Algebraic Aspects of combined matrices |
| topic | Number Theory Combinatorics (Primary) 15A18 (Secondary) 05E99 |
| url | https://arxiv.org/abs/2202.06848 |