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本书叙述深入浅出，以矩阵为主线，突出矩阵的运算和化简，突出用矩阵方法研究线性方程组、二次型和实际问题模型。本书对于抽象的理论和方法，总是从具体问题入手，再将其推广到一般情形，而略去了许多繁杂的理论推导，并力求将数学与应用相结合。 本书的主要内容包括线性方程组、矩阵代数、行列式、向量空间、矩阵的特征值与特征向量和二次型等。 本书是一本介绍性的线性代数教材，内容简洁，层次清晰，适合高等学校理工科专业线性代数课程双语教学使用。 The matrix is the mainline of the book. With the help of the matrix operation and the matrix simplification, we study the linear equations, the quadratic forms and the real world applications. For the purpose of the insights into the abstract theory and the methods of the linear algebra, we start to discuss the conceptions and the methods with the specific problems, then we directly extend them to the general situation without the complicated theoretical derivation. Furthermore, we try to combine the mathematical methods with the real applications in this book. The main contents of the book are linear equations, matrix algebra, determinants, vector spaces, eigenvalues and eigenvectors，and quadratic forms, etc.