Machine Learning Foundations: Linear Algebra

Explore the fundamentals of linear algebra, the mathematical foundation of machine learning algorithms.

Introduction

• Introduction
• What you should know

1. Introduction to Linear Algebra

• Defining linear algebra
• Applications of linear algebra in ML

2. Vectors Basics

• Introduction to vectors
• Vector arithmetic
• Coordinate system

3. Vector Projections and Basis

• Dot product of vectors
• Scalar and vector projection
• Changing basis of vectors
• Basis, linear independence, and span

4. Introduction to Matrices

• Matrices introduction
• Types of matrices
• Types of matrix transformation
• Composition or combination of matrix transformations

5. Gaussian Elimination

• Solving linear equations using Gaussian elimination
• Gaussian elimination and finding the inverse matrix
• Inverse and determinant

6. Matrices from Orthogonality to Gram–Schmidt Process

• Matrices changing basis
• Transforming to the new basis
• Orthogonal matrix
• Gram–Schmidt process

7. Eigenvalues and Eigenvectors

• Introduction to eigenvalues and eigenvectors
• Calculating eigenvalues and eigenvectors
• Changing to the eigenbasis
• Google PageRank algorithm

Conclusion

• Next steps