🧮 Linear Algebra for AI/ML
Linear algebra is a core mathematical foundation for machine learning. Most datasets and models are represented using vectors and matrices, which allow efficient computation, data manipulation, and optimization.
Key concepts such as vectors, matrices, transformations, eigenvalues, and decompositions simplify dimensionality reduction, optimization, and model training.
Algorithms like PCA, SVD, regression, SVMs, and neural networks rely heavily on linear algebra.
Fundamental Concepts (Overview)
- Vectors, matrices, and scalars – basic data representations in ML
- Linear transformations – manipulate data while preserving linearity
- Matrix operations – multiplication, transpose, inverse, determinant
- Eigenvalues & eigenvectors – used in dimensionality reduction and stability
- Norms & distances – measure similarity and differences between data points
- SVD & tensor operations – advanced decomposition for feature extraction and deep learning
Chapters Roadmap
📌 Suggested Learning Flow
- Vectors → operations
- Matrices → multiplication, transpose
- Determinants → inverse, properties
- Linear transformations → visualization
- Vector spaces & rank
- Eigenvalues & eigenvectors
- Norms & distances
- SVD & tensor basics
📚 Recommended Resources
- Book: Linear Algebra and Its Applications by Gilbert Strang
- YouTube: 3Blue1Brown’s series “Essence of Linear Algebra”
- YouTube: Khan Academy (step-by-step basics)
- Practice: Implement concepts using Python/NumPy
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