Mathematics for Data Science and GenAI

What is Linear Algebra ?

Linear Algebra is a branch of math that deals with numbers organised in lines, tables, and grids — called vectors and matrices — and how we can transform them.

It’s the math behind how computers understand and manipulate data — especially in machine learning, AI, image processing, and statistics.

Fundamental Concepts of Linear Algebra for Data Science

1. Scalars

2. Vectors

3. Matrices

4. Tensors

5. Linear Transformations

6. Systems of Linear Equations

7. Eigenvalues and Eigenvectors

8. Determinants

Top Applications of Linear Algebra for Data Science

1. Machine Learning

Used in: Training models like linear regression, neural networks, PCA
How: Datasets are stored as matrices. Matrix operations like dot products help calculate predictions and update model weights.

2. Data Representation

Used in: Storing and transforming large datasets
How: Rows of a matrix = data samples (like customers); columns = features (like age, income).

3. Computer Graphics

Used in: Image processing, 3D graphics, video games
How: Coordinates of objects are stored as vectors. Transformations (rotate, scale, translate) are done using matrix multiplication.

4. Natural Language Processing (NLP)

Used in: Sentiment analysis, translation, chatbots
How: Words are converted into vectors (word embeddings). Matrix operations help understand word similarity and context.

5. Recommender Systems

Used in: Netflix, Amazon, Spotify
How: Ratings and interactions are stored in matrices. Techniques like matrix factorization predict missing values (e.g., "You may also like").

6. Dimensionality Reduction

Used in: Removing noise, compressing data
How: PCA uses eigenvectors and eigenvalues to project high-dimensional data into fewer dimensions.

7. Computer Vision

Used in: Facial recognition, object detection, medical imaging
How: Images are 2D or 3D matrices (tensors). Algorithms process these matrices using filters and transformations.

8. Optimisation Algorithms

Used in: Model training (gradient descent)
How: Derivatives, gradients, and matrix calculus are used to minimize cost/loss functions.

Linear Algebra for Data Science

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