标题： 关于仿射齐次多项式中心对称矩阵 显示英文标题

标题： On affine homogeneous polynomial centrosymmetric matrices

摘要： 我们研究了一类中心对称矩阵，其元素是两个变量的多项式，称为DNA矩阵。 我们的动机源于这些矩阵与洛伦兹旋转作用于平面下的不变多项式之间的意外联系。 在多个值得注意的性质中，我们证明在DNA矩阵的一个子类中，当矩阵阶数为偶数时，奇异矩阵恰好出现，并且在这些情况下确定了它们的零空间。 这些结果为中心对称矩阵的结构特性提供了新的见解，扩展了它们的理论基础和潜在应用。 显示英文摘要

摘要： We explore a class of centrosymmetric matrices whose entries are polynomials in two variables, referred to as DNA matrices. Our motivation stems from an unexpected connection between these matrices and invariant polynomials under the action of a Lorentz rotation on the plane. Among several noteworthy properties, we establish that within a subclass of DNA matrices, singular matrices occur precisely when their order is even, and we determine their null space in such cases. The results provide new insights into the structural characteristics of centrosymmetric matrices, expanding their theoretical foundations and potential applications.