Linear Algebra Notes | 3Blue1Brown Essence of Linear Algebra

Comprehensive Lecture Notes in English & Persian | یادداشت‌های جبر خطی

Complete PDF lecture notes for Grant Sanderson's famous Essence of Linear Algebra video series. Available in English and Persian (فارسی).

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📥 Download PDFs

Language	Pages	Download
English	77	📄 Download PDF
Persian (فارسی)	78	📄 Download PDF

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📚 What's Inside

These notes cover all core concepts of linear algebra with emphasis on geometric intuition - the signature teaching style of 3Blue1Brown.

Topics Covered

Chapter	Topic	Key Concepts
1	Vectors	Vector basics, coordinate systems, vector addition
2	Linear Combinations	Span, basis vectors, linear independence
3	Linear Transformations	Matrix representation, transformation visualization
4	Matrix Multiplication	Composition of transformations, 3D transformations
5	Determinants	Area/volume scaling, orientation
6	Inverse Matrices	Column space, null space, rank
7	Dot Products	Projections, duality
8	Cross Products	3D perpendicular vectors, applications
9	Cramer's Rule	Solving linear systems geometrically
10	Change of Basis	Coordinate transformations
11	Eigenvectors & Eigenvalues	Special directions, characteristic equation
12	Abstract Vector Spaces	Beyond arrows, function spaces

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✨ Features

• 🎯 Geometric Intuition - Visual understanding of every concept
• 📐 Rigorous Definitions - Precise mathematical formulations
• 💡 Practical Applications - Physics, computer graphics, machine learning
• ✏️ Exercises - Practice problems with varying difficulty
• 🎨 TikZ Diagrams - Beautiful vector and transformation visualizations

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🔧 Build from Source

English Version

cd english_notes
pdflatex main.tex
pdflatex main.tex  # Run twice for references

Persian Version

Requires XeLaTeX with XePersian package.

cd persian_notes
xelatex main.tex
xelatex main.tex  # Run twice for references

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📁 Project Structure

├── english_notes/
│   ├── main.tex                                 # Main document
│   ├── preamble.tex                             # LaTeX configuration
│   ├── commands.tex                             # Math macros
│   ├── Linear-Algebra-3Blue1Brown-English.pdf  # Compiled PDF
│   └── lectures/                                # 12 chapter files
│
├── persian_notes/
│   ├── main.tex                                 # Main document
│   ├── preamble.tex                             # XePersian configuration
│   ├── commands.tex                             # Math macros
│   ├── Linear-Algebra-3Blue1Brown-Persian.pdf  # Compiled PDF
│   ├── lectures/                                # 12 chapter files
│   └── figures/                                 # Images

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🇮🇷 نسخه فارسی

این یادداشت‌ها ترجمه کامل مجموعه ویدیویی ذات جبر خطی از کانال 3Blue1Brown هستند.

ویژگی‌ها

• شهود هندسی برای همه مفاهیم
• تعاریف دقیق ریاضی
• مثال‌های کاربردی از فیزیک و علوم کامپیوتر
• تمرین‌های متنوع

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👥 Credits

Sharif University of Technology Physics Association انجمن علمی فیزیک دانشگاه صنعتی شریف

Contributors:

• Ebrahim Khosravani (ابراهیم خسروانی)
• Mohammadhasan Shiri (محمدحسن شیری)
• Zahra Amiri (زهرا امیری)
• Amin Azizi (امین عزیزی)
• Bita Qorbani (بیتا قربانی)
• Yasamin Yazdani (یاسمین یزدانی)
• Sepehr Talaei (سپهر طلایی)

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🔗 Resources

• Original Video Series: Essence of Linear Algebra - 3Blue1Brown
• Creator: Grant Sanderson
• Channel: 3Blue1Brown

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📄 License

This work is for educational purposes. The original video content belongs to 3Blue1Brown.

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Keywords: Linear Algebra, 3Blue1Brown, Essence of Linear Algebra, Math Notes, Lecture Notes, Eigenvectors, Eigenvalues, Matrices, Vectors, Determinants, PDF, LaTeX, Persian, Farsi, English, Grant Sanderson, Mathematics Education, STEM