论文标题
组合矩阵的代数方面
Algebraic Aspects of combined matrices
论文作者
论文摘要
在这项工作中，我们提出了有关组合矩阵$ \ MATHCAL {C}（a）$的代数结果，其中$ a $的条目属于数字字段$ k $，而$ a $是一个非符号矩阵。换句话说，$ a $是属于$ k $的通用线性群的$ n \ times n $矩阵，由$ \ mathrm {gl} _n（k）$表示。我们还分析了矩阵$ a $属于$ \ mathrm {gl} _n（k）$的代数子组，例如单模型组，其中$ a^2 $是$ n \ times n $矩阵，属于特殊的lineart，由$ \ mathrm中的$ \ m ixrian组成的组成部分， 其他的。特别是，我们对对称和非对称矩阵的情况进行了$ n = 2 $和$ n = 3 $的案例，提供了$ \ Mathcal {C}（a）$的显式对角度化，其中包括具有特征性的多项式及其特征性和特征性和特征性的。
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.
