【硬核书】矩阵代数基础，248页pdf

本书涵盖处理矩阵和线性代数的基本原理。它涵盖求解线性方程组，矩阵算术，行列式，特征值，和线性变换。在易于阅读的文本中给出了许多例子。第三版修正了文本中的几个错误并更新了字体。

作者在前言中明确指出，本文不是线性代数。它避免了很多线性代数相关的理论; 尽管如此，作者还是在必要的时候提到了定理。避免使用理论但使用“定理”这一术语可能需要在课堂上进行一些教科书中避免的讨论。

记住，这本书的重点是计算而不是理论，它涵盖了矩阵代数的主要计算方面。虽然作业使用非方阵，但在例子中矩阵乘法部分重点强调方阵。

1 Systems of Linear Equations

1.1 Introduction to Linear Equations

1.2 Using Matrices To Solve Systems of Linear Equations

1.3 Elementary Row Operations and Gaussian Elimination

1.4 Existence and Uniqueness of Solutions

1.5 Applications of Linear Systems

2 Matrix Arithmetic

2.1 Matrix Addition and Scalar Multiplication

2.2 Matrix Multiplication

2.3 Visualizing Matrix Arithmetic in 2D

2.4 Vector Solutions to Linear Systems

2.5 Solving Matrix Equations AX = B

2.6 The Matrix Inverse

2.7 Properties of the Matrix Inverse

3 Operations on Matrices

3.1 The Matrix Transpose

3.2 The Matrix Trace

3.3 The Determinant

3.4 Properties of the Determinant

3.5 Cramer’s Rule

4 Eigenvalues and Eigenvectors

4.1 Eigenvalues and Eigenvectors

4.2 Properties of Eigenvalues and Eigenvectors

5 Graphical Explorations of Vectors

5.1 Transformations of the Cartesian Plane

5.2 Properties of Linear Transformations

5.3 Visualizing Vectors: Vectors in Three Dimensions