Module Overview: Linear Algebra Foundation
This module provides the essential mathematical framework for students and professionals seeking to master Data Analytics and Data Science. Linear Algebra is not merely a theoretical subject; it is the fundamental tool used to structure, manipulate, and interpret the massive, complex, multidimensional datasets encountered in real-world applications. A solid grasp of these concepts is crucial for understanding how modern machine learning algorithms—from simple regression to deep learning networks—process information. This foundational knowledge ensures you can interpret models and handle high-dimensional feature spaces effectively.
đź’ˇ Data Science Perspective
In Data Science, Linear Algebra shifts focus: vectors are viewed as data points or feature lists, rather than purely geometric objects. This perspective is vital for grasping dimensionality reduction (PCA) and model training.
The Role of Linear Algebra
- Data Representation: LA provides the essential language for describing and manipulating complex multidimensional data structures.
- Vectors (Data Points): Used to represent individual records, features, or even functions, serving as the fundamental unit of data in LA.
- Matrices (Datasets): Used to organize entire datasets, where rows typically correspond to individual records and columns correspond to features.
Core Learning Objectives (LA Fundamentals)
- Define Vectors and Matrices and their properties (dimensions, entries).
- Calculate Norms and Distances to measure vector magnitude and separation.
- Perform Fundamental Arithmetic (Addition, Scalar Multiplication).
- Execute key vector products: Hadamard (Element-wise), Dot (Inner), and Outer Products.
- Understand how LA principles derive Similarity Metrics like Cosine Similarity.
Python Implementation