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Linear Algebra for Machine Learning
Essential linear algebra concepts and their applications in machine learning
Core Concepts
1. Vectors and Matrices
- Vector operations (addition, multiplication, dot product)
- Matrix operations (addition, multiplication, transpose)
- Special matrices (identity, diagonal, symmetric)
- Applications in feature representation and transformations
2. Linear Transformations
- Matrix transformations
- Eigenvalues and eigenvectors
- Singular Value Decomposition (SVD)
- Applications in dimensionality reduction (PCA)
3. Vector Spaces
- Basis and dimension
- Orthogonality and projections
- Span and linear independence
- Applications in feature selection and representation
4. Matrix Decompositions
- LU decomposition
- QR decomposition
- Cholesky decomposition
- Applications in solving linear systems and optimization
Practical Applications
- Neural network weight matrices
- Image processing and computer vision
- Natural language processing (word embeddings)
- Dimensionality reduction techniques
- Optimization algorithms