Module 3: Linear Algebra

In this module, you will learn about the fundamentals of linear algebra and its applications in data science. You'll explore vectors, matrices, linear transformations, and how they relate to linear regression models. These concepts form the mathematical foundation for many machine learning algorithms.

Objective 1: Define vectors, vector length and dot product

Learn the fundamental vector concepts that form the basis of linear algebra.

• Understanding vectors and their properties
• Calculating vector length (magnitude)
• Computing dot products between vectors
• Applying vector operations in data science contexts

Objective 2: Define a matrix, transpose and inverse

Learn about matrices and key matrix operations essential for data analysis.

• Understanding matrix structure and notation
• Performing matrix transposition
• Calculating matrix inverses
• Applying matrix operations to datasets

Objective 3: Use linear algebra to solve for coefficients

Learn how to apply linear algebra techniques to solve for regression coefficients.

• Representing regression problems in matrix form
• Deriving the normal equation using linear algebra
• Solving for coefficients using matrix operations
• Implementing the closed-form solution for linear regression

Objective 4: Explain cosine similarity

Learn about cosine similarity and its applications in measuring vector relationships.

• Understanding the concept of vector similarity
• Calculating cosine similarity between vectors
• Interpreting cosine similarity values
• Applying cosine similarity in text analysis and recommendations

Linear Algebra

Resources:

The notebook for this guided project is DS_133_Linear_Algebra.ipynb in the GitHub repository.

Linear Algebra Assignment

In this module assignment, found in the file DS_133_Linear_Algebra_Assignment_AG.ipynb in the GitHub repository, you'll apply your knowledge of linear algebra to data science problems:

Tasks:

1. Implement vector and matrix operations
2. Use linear algebra to implement linear regression
3. Solve systems of linear equations using matrices
4. Apply linear algebra concepts to analyze datasets
5. Use linear transformations to manipulate data