├── Introduction to Liner algebra Syllabus.pdf
├── Introduction_to_Linear_algebra_for_AI.pdf
└── README.md


/Introduction to Liner algebra Syllabus.pdf:
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/Introduction_to_Linear_algebra_for_AI.pdf:
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https://raw.githubusercontent.com/shining0611armor/Introduction_of_linear_algebra_for_AI/b976fa17edbe0158edce84a386abdf3433c7eacb/Introduction_to_Linear_algebra_for_AI.pdf


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/README.md:
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  1 | # 📘 Introduction to Linear Algebra for AI
  2 | 
  3 | Welcome to the **Introduction to Linear Algebra for AI** course! This course is designed to provide a comprehensive understanding of linear algebra concepts crucial for artificial intelligence and machine learning.
  4 | 
  5 | ## 📜 Syllabus
  6 | 
  7 | ### Part A: Basics of Linear Algebra
  8 | - **What is Vector, Matrix, Tensor?**
  9 | - **Vector Space**:
 10 |   - Space, vector space
 11 |   - Linear combination
 12 |   - Span
 13 |   - Linear dependence and independence
 14 |   - Basis
 15 |   - Dimension
 16 | - **Column and Row Vectors**:
 17 |   - Span in matrix form
 18 |   - Column space
 19 |   - Row space
 20 |   - Null vector and null space
 21 |   - Left null space
 22 |   - Operations on matrices (matrix multiplication, vectorization, and Hadamard product)
 23 |   - Inner and outer product
 24 | - **Rank**:
 25 |   - Column rank, row rank, rank, full rank
 26 |   - Fat and thin matrix
 27 |   - Rank deficient, singular, nonsingular, inverse
 28 | - **Orthogonality**:
 29 |   - Length of vector
 30 |   - Orthogonal vector, orthogonal basis
 31 |   - Orthonormal
 32 |   - Orthogonal matrix
 33 |   - Gram-Schmidt orthogonalization
 34 | - **Functions in Linear Algebra**:
 35 |   - Affine function
 36 |   - Quadratic function
 37 | 
 38 | ### Part B: Norms & Normalizations
 39 | - **Vector Norms**:
 40 |   - LP-norms
 41 | - **Matrix Norms**:
 42 |   - Frobenius norm
 43 |   - Spectral norm
 44 |   - Nuclear norm
 45 | - **Importance of Normalization in Machine Learning**:
 46 |   - Batching data
 47 |   - Batch norm
 48 |   - Layer norm
 49 |   - Standardization
 50 |   - Comparison
 51 | 
 52 | ### Part C: Equations
 53 | - **Systems of Equations**:
 54 |   - Under-determined system
 55 |   - Over-determined system
 56 | - **Linear Equations**:
 57 |   - Full rank case
 58 |   - Low rank (rank deficient) case
 59 |   - Noisy case
 60 |   - Least squares method
 61 | 
 62 | ### Part D: Eigens and Positive Definity
 63 | - **Eigenvalues and Eigenvectors**:
 64 |   - Algebraic multiplicity
 65 |   - Geometric multiplicity
 66 |   - Eigenspace
 67 |   - Eigen decomposition
 68 | - **Positive Definite and Positive Semi-Definite**:
 69 |   - Properties of PD and PSD matrices
 70 | 
 71 | ### Part E: SVD & Special Matrices
 72 | - **Singular Value Decomposition (SVD)**:
 73 |   - SVD
 74 |   - Skinny SVD
 75 |   - Compact SVD
 76 | - **Statistics and Matrices**:
 77 |   - Normal distribution
 78 |   - Variance
 79 |   - Covariance matrix
 80 |   - Correlation matrix
 81 |   - Modal matrix
 82 |   - Making features of datasets independent
 83 |   - Properties of eigenvalues and eigenvectors of covariance matrix
 84 |   - Scale invariant
 85 |   - Translation invariant
 86 |   - Rotation invariant
 87 |  
 88 | 
 89 | ### Part F: Additional Topics
 90 | - **Data Storage**:
 91 |   - Storing data row major
 92 | - **Vectorization**:
 93 |   - Vectorization in numpy
 94 | 
 95 | > **Note**: This course does not cover other study topics such as functions, transformations, eliminations, decompositions, projections, and multivariate calculus (Gradient, Hessian, Jacobian).
 96 | 
 97 | ## 🌟 Key Features
 98 | - 📚 Comprehensive content tailored for AI enthusiasts
 99 | - 🔍 Detailed explanations with practical examples
100 | - 🧮 Mathematical foundations essential for machine learning
101 | 
102 | ## 📫 Contact
103 | Feel free to reach out if you have any questions or suggestions:
104 | - **Email**: mehrant.0611@gmail.com
105 | - **GitHub**: [shining0611armor](https://github.com/shining0611armor)
106 | 
107 | ---
108 | 
109 | Happy Learning! 😊
110 | 


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