線性代數 (Linear Algebra) from Udemy

超過 22 小時的超詳細線性代數課程，帶你一步步學會線性代數的重要觀念和公式，趕快收藏起來.

這門詳盡的線性代數課程將引領您深入瞭解多個主題，包括機器學習中的主成分分析（Principal Component Analysis, PCA）、Python 實作的圖像分析、馬可夫鏈、SVD分解、LU分解、QR分解、特徵值和特徵向量、施特拉森演算法、可逆矩陣的判斷以及Gershgorin圓定理。

線性代數為電腦科學、資訊工程等領域的必修課程，其應用之廣泛，包含機器學習、深度學習、預測模型、電腦圖形處理以及加密系統等等。這堂線性代數課程內容包含基本的線性方程組的基本運算、向量空間、線性獨立、矩陣的可逆性、行列式、線性轉換、還有特徵矩陣以及特徵值的尋找，一步一步帶你認識所有重要的觀念、證明、運算過程與題目解答。不論你的數學基礎為何，都可以有系統性的認識線性代數中的重要理論、公式與計算原理。所有課程中所提到的公式與定理皆有證明過程與對應例子，讓學習有紮實基礎！

另外，課程也包含線性代數在電腦科學中的應用，包含密碼學的加密與解密演算法、圖形與向量處理、2D旋轉壓縮移動矩陣、3D旋轉矩陣、主成分分析 (PCA) 等等。這堂課程也包含章節的練習題，讓你能夠衡量學習成效與得到充分練習的機會。

你應該要註冊這堂課的理由:

超過 22 小時的超詳細線性代數課程，帶你一步步學會線性代數的重要觀念和公式，趕快收藏起來.

你應該要註冊這堂課的理由:

課程教材適合所有程度的人，不論你的數學基礎為何，此課程由簡入深學習所有必要資訊與觀念.
課程涵蓋其他線性代數的補充與電腦科學應用。
學會用Geogebra軟體來輔助了解空間與矩陣運算。

What's inside

Syllabus

Chapter 0 - Course Preparation

Learning Tips

Course Resources

Chapter 1 - Linear Equations

Note on 0

Symbols and Sets

Solving Linear Equations

Row Reduction

Practice Questions

Reduced Row Echelon Form

RREF Algorithm

Quick Fix

RREF Reasoning

Vectors

Linear Combinations

Span of Vectors

Video Recommendation

Matrix-Vector Multiplication

Properties of Ax=b

Matrix Multiplication

Reachability Matrix

Homogeneous Linear Systems

Applications of Linear System

Linear Independence

Theorem 證明補充

Solution Sets to Ax=b

Introduction to transformation

Uniqueness of Pre-image

Rotation Matrix

Matrix for transformation

Relations of Domain and Codomain

Chapter 2 - Matrix Algebra

Matrix Operations

Transpose of Matrix

Inverse Matrix

The Uniqueness of Inverse Matrix

Algorithm of Producing an Inverse Matrix

Cost of Producing Inverse Matrix

Characterization of Invertible Matrix

Invertible matrix examples

Polyalphabetic Cryptosystem

Polyalphabetic程式碼

Partitioned Matrix

Strassen Algorithm

LU Factorization

LU Factorization Reasoning

Leontief Model Part 1

Leontief Model Part 2

Computer Graphics

Subspaces in R^n

Coordinate System

The Rank-Nullity Theorem

Chapter 3 - Determinants

Work and Dot Product

Properties of Dot Product

Schwarz Inequality

Cross Product

Introduction to Determinants

Examples

Basic definition of determinant

Properties Part 1

Properties Part 2

Quick Note

Cramer's Law

Cross Product Formula

Parallelepiped Volume

Google Form

Chapter 4 - Vector Space in General

Vector Space in General

Linear Transformation in General

Linearly Independent Set, Basis

The Unique Representation Theorem

Coordinate Mapping

x to [x]B

Bijective Linear Transformation

Theorems

Dimension and Rank

Change of Basis

Application to Markov Chain

Chapter 5 - Eigenvectors and Eigenvalues

Eigenvectors and Eigenvalues

Theorems of Eigenvectors

Eigenvectors and Markov Chain

Diagonalization Theorem

[x]_B to [T(x)]_C

Theorem

Complex Eigenvectors

Rotation and Stretch Behavior

The Power Method

Shifted Inverse Power Method

Gershgorin Circle Theorem

Chapter 6 - Inner Product Space

Inner Product

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

這門課程其中一個主題是廣泛應用的線性代數在電腦圖形處理中。

這門課程涵蓋了深入線性代數多個領域的主題，包含機器學習中的主成分分析（Principal Component Analysis, PCA）、Python 實作的圖像分析、馬可夫鏈、SVD分解、QR分解、特徵值和特徵向量、施特拉森演算法等內容。

課程包含章節的練習題，幫助衡量學習進度並得到充足的練習機會。

這門課程包含線性代數在電腦科學中的應用，包含密碼學的加密與解密演算法、圖形與向量處理、2D旋轉與壓縮移動矩陣等內容。

這門課程由淺入深，學習所有重要的線性代數觀念、證明、運算過程與題目解答。

Reviews summary

线性代数基础夯实

根据学生的说法，线性代数课程提供了易懂的基础知识，非常适合初学者。课程内容结构清晰，示例丰富，视频形式的讲解有助于理解。虽然有的同学认为课程内容稍浅，但大部分同学都认为这是一门优质的课程。

视频讲解生动易懂

"I like the way the course is set up. I've found the topics easy to remember so far"

"I love this long course, less things to read and many lectures as videos."

"Sal's background as a teacher really shows in the way she structures her courses and in the way she produces the content. She makes the material engaging and easy to understand."

适合初学者，入门基础讲解清晰

"It was great course for beginners. simple to follow"

"Easy to understand for beginners. Well-structured. Thank you Sal."

"I am a total beginner and the explanations are great to understand the tarot clearly!"

课程内容有些浅显

"The course is good, profound knowledge. I hope it gets more advance when I follow with the rest."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in 線性代數 (Linear Algebra) with these activities:

尋找一位線性代數專家作為指導者

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找到一位優秀的指導者將提供額外的支持和指導，幫助你更深入地探索線性代數。

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詢問教授或助教推薦信
參加相關活動或工作坊，認識潛在的指導者

Show all one activities

Career center

Learners who complete 線性代數 (Linear Algebra) will develop knowledge and skills that may be useful to these careers:

Computer Scientist

Computer Scientists design, develop, and analyze computer systems and software. They work with a variety of programming languages and technologies to create solutions for a wide range of problems. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of computer science. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy computer science models.

See salaries and explore the career path for Computer Scientist

Mathematician

Mathematicians study the properties of numbers, shapes, and patterns. They develop new mathematical theories and techniques to solve problems in a variety of fields. This course will help you build a strong foundation in linear algebra, which is essential for understanding many areas of mathematics. By understanding the concepts in linear algebra, you will be better equipped to pursue a career in mathematics.

See salaries and explore the career path for Mathematician

Statistician

Statisticians collect, analyze, and interpret data. They work with a variety of data sources and tools to identify trends, patterns, and relationships. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of statistics. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy statistical models.

See salaries and explore the career path for Statistician

Data Scientist

Data Scientists combine programming skills with statistical and mathematical knowledge to extract insights from data. They work with a variety of data sources and tools to identify trends, patterns, and relationships. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of data science. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy data science models.

See salaries and explore the career path for Data Scientist

Machine Learning Engineer

Machine Learning Engineers design, develop, and deploy machine learning models. They work with a variety of machine learning algorithms and techniques to build models that can learn from data and make predictions. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of machine learning. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy machine learning models.

See salaries and explore the career path for Machine Learning Engineer

Actuary

Actuaries use mathematical and statistical models to assess risk and uncertainty. They work with a variety of data sources and tools to develop and implement risk management strategies. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of actuarial science. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy actuarial models.

See salaries and explore the career path for Actuary

Risk Manager

Risk Managers use mathematical and statistical models to assess risk and uncertainty. They work with a variety of data sources and tools to develop and implement risk management strategies. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of risk management. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy risk management models.

See salaries and explore the career path for Risk Manager

Economist

Economists study how people make decisions in the face of scarcity. They develop models to explain economic phenomena and make predictions about the future. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of economics. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy economic models.

See salaries and explore the career path for Economist

Physicist

Physicists study the laws of nature. They develop models to explain the behavior of matter and energy. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of physics. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy physics models.

See salaries and explore the career path for Physicist

Engineer

Engineers design, build, and maintain structures and systems. They work with a variety of materials and technologies to create solutions for a wide range of problems. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of engineering. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy engineering models.

See salaries and explore the career path for Engineer

Operations Research Analyst

Operations Research Analysts use mathematical and statistical models to optimize business processes. They work with a variety of data sources and tools to identify inefficiencies and develop solutions. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of operations research. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy operations research models.

See salaries and explore the career path for Operations Research Analyst

Data Analyst

Data Analysts collect, clean, and analyze data to extract meaningful insights. Their work helps businesses make informed decisions about products, marketing, and operations. This course will build a strong foundation in linear algebra, which is essential for understanding data structures, algorithms, and statistical models. By understanding the concepts in linear algebra, you will be better equipped to analyze large datasets and draw meaningful conclusions.

See salaries and explore the career path for Data Analyst

Financial Analyst

Financial Analysts use mathematical and statistical models to analyze financial data and make investment decisions. They work with a variety of data sources and tools to identify trends, patterns, and relationships. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of financial analysis. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy financial analysis models.

See salaries and explore the career path for Financial Analyst

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data and make investment decisions. They work with a variety of data sources and tools to identify trends, patterns, and relationships. This course will help you build a strong foundation in linear algebra, which is essential for understanding the mathematical foundations of quantitative finance. By understanding the concepts in linear algebra, you will be better equipped to develop and deploy quantitative finance models.

See salaries and explore the career path for Quantitative Analyst

Software Engineer

Software Engineers design, develop, and maintain software applications. They work with a variety of programming languages and technologies to create solutions for a wide range of problems. This course will help you build a strong foundation in linear algebra, which is essential for understanding computer graphics, image processing, and machine learning algorithms. By understanding the concepts in linear algebra, you will be better equipped to develop robust and efficient software applications.

See salaries and explore the career path for Software Engineer