# 一些线性代数的资源

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# Introduction to Linear Algebra 5th

MIT18.06 的 TextBook。

• Introduction to vectors
• Solving Linear Equations
• Vector Spaces and Subspaces
• Orthogonality
• Determinants
• Eigenvalues and Eigenvectors
• The Singular Value Decomposition
• Linear Transformations
• Complex Vectors and Matrices
• Applications
• Numerical Linear Algebra
• Linear Algebra in Probability and Statistics

# MIT18.065

Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

# Linear Algebra and Learning From Data

MIT18.065 的 TextBook。

7个章节：

1. 线性代数重点
2. 计算大型矩阵
3. 低秩与压缩感知
4. 特殊矩阵
5. 概率与统计
6. 优化
7. 从数据中学习

# 2020线性代数新视野

• 线性代数的新方法
• 矩阵的列空间与向量空间中的基
• 线性代数的 Big Picture
• 正交向量
• 特征值与特征向量
• 奇异值与奇异向量

# 沉浸式线性代数

• Chapter 1: Introduction

How to navigate, notation, and a recap of some math that we think you already know.

• Chapter 2: Vectors

The concept of a vector is introduced, and we learn how to add and subtract vectors, and more.

• Chapter 3: The Dot Product

A powerful tool that takes two vectors and produces a scalar.

• Chapter 4: The Vector Product

In three-dimensional spaces you can produce a vector from two other vectors using this tool.

• Chapter 5: Gaussian Elimination

A way to solve systems of linear equations.

• Chapter 6: The Matrix

Enter the matrix.

• Chapter 7: Determinants

A fundamental property of square matrices.

• Chapter 8: Rank

Discover the behaviour of matrices.

• Chapter 9: Linear Mappings

Learn to harness the power of linearity…

• Chapter 10: Eigenvalues and Eigenvectors

This chapter has a value in itself.

# 交互式线性代数

• Systems of Linear Equations: Algebra
• Systems of Linear Equations
• Row Reduction
• Parametric Form
• Systems of Linear Equations: Geometry
• Vectors
• Vector Equations and Spans
• Matrix Equations
• Solution Sets
• Linear Independence
• Subspaces
• Basis and Dimension
• Bases as Coordinate Systems
• The Rank Theorem
• Linear Transformations and Matrix Algebra
• Matrix Transformations
• One-to-one and Onto Transformations
• Linear Transformations
• Matrix Multiplication
• Matrix Inverses
• The Invertible Matrix Theorem
• Determinants
• Determinants: Definition
• Cofactor Expansions
• Determinants and Volumes
• Eigenvalues and Eigenvectors
• Eigenvalues and Eigenvectors
• The Characteristic Polynomial
• Similarity
• Diagonalization
• Complex Eigenvalues
• Stochastic Matrices
• Orthogonality
• Dot Products and Orthogonality
• Orthogonal Complements
• Orthogonal Projection
• Orthogonal Sets
• The Method of Least Squares

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