Linear Algebra for ML
This path demystifies linear algebra, focusing on the core concepts essential for understanding and building machine learning algorithms. You'll learn the intuitions behind vectors, matrices, and transformations, and how they power everything from data representation to neural networks.
Sessions
Linear Algebra: Vectors
After this session, you'll be able to explain what a vector is, its geometric meaning, and how basic vector operations represent data features and relationships.
10 min
Matrices as Transformations
You'll be able to explain how matrices act as transformations on vectors, and the geometric intuition behind matrix-vector and matrix-matrix multiplication.
10 min
Linear Transformations & Basis
You will understand what defines a linear transformation, and the concepts of vector spaces, subspaces, and basis vectors.
10 min
Eigenvalues & Eigenvectors
You'll be able to explain eigenvalues and eigenvectors as special vectors that only scale under a linear transformation, and why they are important for understanding system dynamics.
10 min
Orthogonality & Projections
You'll be able to explain orthogonal vectors, orthonormal bases, and how projections allow us to find the 'closest' point in a subspace.
10 min
Singular Value Decomposition
You will understand the Singular Value Decomposition (SVD) as a powerful matrix factorization and its geometric interpretation, connecting it to dimensionality reduction.
10 min
What you'll achieve
Understand vector operations and their geometric interpretations as data points and features.
Grasp matrix multiplication and its role in transforming data, such as scaling, rotation, and projection.
Comprehend linear transformations, vector spaces, and basis vectors as frameworks for data representation.
Learn about eigenvalues and eigenvectors as fundamental properties revealing invariant directions of transformations.
Understand the concept of orthogonality and projections, crucial for optimization and dimensionality reduction.
Explain the Singular Value Decomposition (SVD) and its applications in practical machine learning scenarios like PCA.