# Linear Algebra for Machine Learning and Quantum Computing

- Institution: IIT Indore
- Department: Mathematics
- Teacher: Prof. Ranveer Singh
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106004)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106004)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course develops linear algebra with a clear focus on computation and applications in computer science. We build from vector spaces, inner products, and orthogonality to projections, least-squares problems, eigenvalues, spectral decompositions, and singular value decomposition (SVD). Using these tools, we study data matrices, covariance, principal component analysis (PCA), linear regression, and Markov chains with applications such as PageRank. In the final module, we introduce complex vector spaces, quantum states, basic quantum gates, and simple quantum circuits to show how linear algebra underlies both modern machine learning and quantum computing. The course emphasizes conceptual understanding through worked examples and applications, providing a solid foundation for further study in ML, data science, and quantum information.

Intended audience: B.Tech / M.Tech / M.Sc in CS

Prerequisites: Educational level: At least 1st year UG (or above) in CSE/IT/ECE/EE/Math.Mathematical background: Basic calculus, high-school algebra.

## Lectures

1. [Matrix product as linear combinations](https://invisiblenetwork.ai/learn/nptel/111106004/1abd95376fd1) (YouTube)
2. [Linear dependence and bases](https://invisiblenetwork.ai/learn/nptel/111106004/155c6821effe) (YouTube)
3. [Inner products and projections](https://invisiblenetwork.ai/learn/nptel/111106004/5cfddde98900) (YouTube)
4. [Projection onto subspaces and projection matrices](https://invisiblenetwork.ai/learn/nptel/111106004/3fc44be68fe6) (YouTube)
5. [Least squares problems, reflections, rotations](https://invisiblenetwork.ai/learn/nptel/111106004/df3c11c06123) (YouTube)
6. [Gram-Schmidt orthogonalization and QR decomposition](https://invisiblenetwork.ai/learn/nptel/111106004/7a88653c96fe) (YouTube)
7. [Four fundamental subspaces and their orthogonality](https://invisiblenetwork.ai/learn/nptel/111106004/f3fbb67900db) (YouTube)
8. [Matrix rank and the rank-nullity theorem](https://invisiblenetwork.ai/learn/nptel/111106004/6eb084fb4cb9) (YouTube)
9. [Gaussian elimination, pivots, and computing rank](https://invisiblenetwork.ai/learn/nptel/111106004/afed7c1d4e4d) (YouTube)
10. [Matrix inverses and rank tests for linear systems](https://invisiblenetwork.ai/learn/nptel/111106004/6277e3a10854) (YouTube)
11. [Least-squares linear regression and normal equations](https://invisiblenetwork.ai/learn/nptel/111106004/aa5cc31d9c46) (YouTube)
12. [Determinants, elimination, and invertibility](https://invisiblenetwork.ai/learn/nptel/111106004/429d4512364d) (YouTube)
13. [Eigenvalues, eigenvectors, and the characteristic equation](https://invisiblenetwork.ai/learn/nptel/111106004/76be167eab78) (YouTube)
14. [Diagonalization using eigenvectors, matrix powers, and long-term behavior](https://invisiblenetwork.ai/learn/nptel/111106004/8be08ed34006) (YouTube)
15. [Symmetric matrices, spectral theorem, and orthogonal diagonalization](https://invisiblenetwork.ai/learn/nptel/111106004/1f2f0c0c1b18) (YouTube)
16. [Positive definite matrices, quadratic forms, Cholesky decomposition, and optimization](https://invisiblenetwork.ai/learn/nptel/111106004/ab3eb8e31e73) (YouTube)
17. [Singular value decomposition: singular values, singular vectors, construction, and rank](https://invisiblenetwork.ai/learn/nptel/111106004/b385268a82a5) (YouTube)
18. [Principal component analysis: variance, covariance, projection, and dimensionality reduction](https://invisiblenetwork.ai/learn/nptel/111106004/3ec2e91763d7) (YouTube)
19. [PCA through SVD, low-rank approximation, image compression, and Eckart–Young theorem](https://invisiblenetwork.ai/learn/nptel/111106004/050136cf3fbc) (YouTube)
20. [Random walks, Markov chains, stationary distributions, spectral mixing, and Monte Carlo simulation](https://invisiblenetwork.ai/learn/nptel/111106004/1fd31df3c22b) (YouTube)
21. [Clustering, K-Means, and Introduction to Spectral Clustering](https://invisiblenetwork.ai/learn/nptel/111106004/76037ec9b64c) (YouTube)
22. [Mathematical Reasoning for Spectral Clustering](https://invisiblenetwork.ai/learn/nptel/111106004/6a9591e305b3) (YouTube)
23. [Complex Linear Algebra, Qubits, and Measurement](https://invisiblenetwork.ai/learn/nptel/111106004/ba9a999a0740) (YouTube)
24. [Single-Qubit Gates: Actions and Examples](https://invisiblenetwork.ai/learn/nptel/111106004/268f20c7ac31) (YouTube)
25. [Multi-Qubit States, Gates, and Density Matrices](https://invisiblenetwork.ai/learn/nptel/111106004/d56b2f96d3c2) (YouTube)
26. [Separable States and Entanglement](https://invisiblenetwork.ai/learn/nptel/111106004/8d0558aca34f) (YouTube)