范德蒙德行列式在高等代数解题中的应用

Application of Vandermonde Determinant in Advanced Algebra Solving

摘要: 范德蒙德行列式的结构以及运算结果都具有其独特性，在高等代数中有广泛的应用。本文讨论了范德蒙德行列式在高等代数解题中的应用，具体探讨了范德蒙行列式在多项式、行列式、线性方程组、向量组的线性相关性、线性变换等知识模块中的应用，并选取了部分考研真题以及典型高等代数题目对这些应用进行了详细阐述。

Abstract: The structure and calculation results of Vandermonde determinant are unique, and they are widely used in advanced algebra, calculus and so on. This paper discusses Vandermonde DE determinant in higher algebra problem solving, specifically discussing the application of Vandermonde determinant in polynomial, determinant, linear system of equations, linear correlation of vector group, linear transformation and so on, and selects some of the real exam questions and typical advanced algebra questions to elaborate on these applications.