# Linear_Algebra_With_Python
**Repository Path**: youngday/Linear_Algebra_With_Python
## Basic Information
- **Project Name**: Linear_Algebra_With_Python
- **Description**: 这份讲义共包含 19 个章节，学习者可以使用 Jupyter NBViewer 打开 notebook，或者直接下载学习。
第一讲：线性方程系统
第二讲：基础矩阵代数
第三讲：行列式
第四讲：LU 分解
第五讲：向量运算
第六讲：线性组合
第七讲：线性无关
第八讲：向量空间与子空间
第九讲：基与维度
第十讲：行空间、列空间与零空间
第十一讲：线性变换
第十二讲：特征值与特征向量
第十三讲：对角化
第十四讲：动力系统的应用
第十五讲：内积与正交
第十六讲：Gram-Schmidt 正交化过程与 QR 分解
第十七讲：对称矩阵与二次型
第十八讲：奇异值分解
第十九讲：多变量正态分布
打开对应的 notebook 后，学习者可以看到对线性代数基本概念的讲解，以及代码和图示等。
- **Primary Language**: Unknown
- **License**: MIT
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No
## Statistics
- **Stars**: 0
- **Forks**: 2
- **Created**: 2022-06-05
- **Last Updated**: 2022-06-05
## Categories & Tags
**Categories**: Uncategorized
**Tags**: None
## README
# Lectures of Linear Algebra []()
These lecture notes are intended for introductory linear algebra courses, suitable for university students, programmers, data analysts, algorithmic traders and etc.
The lectures notes are loosely based on several textbooks:
1. Linear Algebra and Its Applications by Gilbert Strang
2. Linear Algebra and Its Applications by David Lay
3. Introduction to Linear Algebra With Applications by DeFranza & Gagliardi
4. Linear Algebra With Applications by Gareth Williams
However, the crux of the course is not about proving theorems, but to demonstrate the practices and visualization of the concepts. Thus we will not engage in strictly precise deduction or notation, rather we aim to clarify the elusive concepts and thanks to Python/MATLAB, the task is much easier now.
## Prerequisites
Though the lectures are for beginners, it is beneficial that attendants had certain amount of exposure to a little linear algebra and calculus before.
And also the attendants are expected to have basic knowledge (3 days training would be enough) of
- [x] Python
- [x] NumPy
- [x] Matplotlib
- [x] SymPy
All the codes are written in an intuitive manner rather than efficient or professional coding style, therefore the codes are exceedingly straightforward, I presume barely anyone would have difficulty in following the codes.
## What to Expect from Notes
These notes will equip you with most needed and basic knowledge for other subjects, such as Data Science, Econometrics, Mathematical Statistics, Control Theory and etc., which heavily rely on linear algebra. Please go through them patiently, you will certainly have a better grasp of the fundamental concepts of linear algebera. Then further step is to study the special matrices and their application with your domain knowledge.
## Contents
It is advisable to either open the notebooks in Jupyter nbviewers (links below) or download them, since github has lots of rendering mistakes in LaTeX and sometimes even missing plots.
[Lecture 1 - System of Linear Equations](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/LinearAlgebraLectures/blob/master/Chapter%201%20-%20Linear%20Equation%20System.ipynb)
[Lecture 2 - Basic Matrix Algebra](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/LinearAlgebraLectures/blob/master/Chapter%202%20-%20Basic%20Matrix%20Algebra.ipynb)
[Lecture 3 - Determinants](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/LinearAlgebraLectures/blob/master/Chapter%203%20-%20Determinant.ipynb)
[Lecture 4 - LU Decomposition](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/LinearAlgebraLectures/blob/master/Chapter%204%20-%20LU%20Factorization.ipynb)
[Lecture 5 - Vector Operations](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%205%20-%20Vector%20Addition%2C%20Subtraction%20and%20Scalar%20Multiplication.ipynb)
[Lecture 6 - Linear Combination](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%206%20-%20Linear%20Combination.ipynb)
[Lecture 7 - Linear Independence](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%207%20-%20Linear%20Independence.ipynb)
[Lecture 8 - Vector Space and Subspace](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%208%20-%20Vector%20Space%20and%20Subspace.ipynb)
[Lecture 9 - Basis and Dimension](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%209%20-%20Basis%20and%20Dimension.ipynb)
[Lecture 10 - Column, Row and Null Space](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%2010%20-Null%20Space%20vs%20Col%20Space%2C%20Row%20Space%20and%20Rank.ipynb?flush_cache=true)
[Lecture 11 - Linear Transformation](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%2011%20-%20Linear%20Transformation.ipynb?flush_cache=true)
[Lecture 12 - Eigenvalues and Eigenvectors](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%2012%20-%20Eigenvalues%20and%20Eigenvectors.ipynb)
[Lecture 13 - Diagonalization](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%2013%20-%20Diagonalization.ipynb)
[Lecture 14 - Application to Dynamic System](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%2014%20-%20Applications%20to%20Dynamic%20System.ipynb)
[Lecture 15 - Inner Product and Orthogonality](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%2015%20-%20Innear%20Product%20and%20Orthogonality.ipynb)
[Lecture 16 - Gram-Schmidt Process and Decomposition](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%2016%20-%20Gram-Schmidt%20Process%20and%20QR%20Decomposition.ipynb)
[Lecture 17 - Symmetric Matrices and Quadratic Form](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%2017%20-%20Symmetric%20Matrices%20%2C%20Quadratic%20Form%20and%20Cholesky%20Decomposition.ipynb)
[Lecture 18 - Singular Value Decomposition](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%2018%20-%20The%20Singular%20Value%20Decomposition.ipynb)
[Lecture 19 - Multivariate Normal Distribution](https://nbviewer.jupyter.org/github/WeijieChen-MacroAnalyst/Linear_Algebra_With_Python/blob/master/Chapter%2019%20-%20Multivariate%20Normal%20Distribution.ipynb)