数代数

一些线性代数的资源

字数统计: 557字   |   阅读时长: 2分
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摘要: 本文介绍一些线性代数的资源

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MIT 18.06

讲义：

Introduction to Linear Algebra 5th

MIT18.06 的 TextBook。

主要内容：

  • 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

主要内容：

  • 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

主要内容：

  • 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

主要内容：

  • 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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