线性代数中基于线性方程组的“转换”思想

Based on the System of Linear Equations' Transform Thought in Linear Algebra

线性代数的主要研究对象是行列式、矩阵、线性方程组、矩阵的特征值、二次型以及线性变换,其中线性方程组的学习和研究贯穿全书。首先我们使用行列式和矩阵作为工具来判断线性方程组的解。之后我们利用"转换"思想把具体的线性问题构建成一个线性方程组的数学模型,将线性问题转化成方程组求解问题。文中列举了线性代数基于线性方程组"转换"思想的三处知识点,分别是:向量组的线性组合、向量组的线性相关性、矩阵的特征值。利用"转换"思想可以加深大家对线性问题的理解。

The main research object of linear algebra is the determinant,matrix,linear equations,the eigenvalues of the matrix,quadratic and linear transformation,the study and research of Linear equations is throughout the book.First we use determinant and matrix as a tool to determine the solution of the linear system of equations.Then we use"transformation"to a built a linear equations mathematical mode which can solve the problem of linear problem,and the linear problem is converted into a linear equations solving problem.The paper enumerates three points based on the"transformation"of linear equations,respectively is:a linear combination of the vectors,the vector group of linear correlation,eigenvalues of the matrix.Using the idea of"transformation"can deepen people's understanding of linear problem.