发表机构
Daugavpils University; Ben-Gurion University of the Negev（道加夫皮尔斯大学; 内盖夫本-古里安大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文比较行列式的不同引入方法，主张基于乘法映射的自然特征定义行列式，以降低认知难度并契合现代数学教育的结构导向。
AI 中文摘要
行列式传统上通过排列展开、多重线性或递归展开公式引入——这些方法虽然严谨，但往往掩盖了其概念意义。相反，本文提倡一种方法，即通过其作为矩阵上乘法映射的自然特征来定义行列式，反映其作为线性变换在复合下结构不变量的作用。这种视角将组合机制推迟到核心性质建立之后，从而降低了初次接触该概念学生的认知障碍。本文展示了该特征化与经典表述的等价性，并论证了这一框架更符合现代数学教育的结构强调。
英文摘要
The determinant is traditionally introduced through permutation expansions, multilinearity, or recursive expansion formulas - approaches that, while rigorous, often obscure its conceptual significance. Instead, an approach is advocated wherein the determinant is defined via its natural characterization as a multiplicatice map on matrices, reflecting its role as a structural invariant of linear transformations under composition. This perspective defers combinatorial machinery until after the core properties are estaqblished, thereby lowering the cognitive barrier for students encountering the concept for the first time. The equivalence of this characterization with classical formulations is shown, and it is argued that this framework better aligns with the structural emphasis of m odern mathematical education.
