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Course11110600426 lectures

Linear Algebra for Machine Learning and Quantum Computing

Prof. Ranveer Singh · IIT Indore

Start with lecture 1 At NPTEL

About

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

Week 1

  1. Matrix product as linear combinations YouTube
  2. Linear dependence and bases YouTube
  3. Inner products and projections YouTube
  4. Projection onto subspaces and projection matrices YouTube
  5. Least squares problems, reflections, rotations YouTube
  6. Gram-Schmidt orthogonalization and QR decomposition YouTube

Week 2

  1. Four fundamental subspaces and their orthogonality YouTube
  2. Matrix rank and the rank-nullity theorem YouTube
  3. Gaussian elimination, pivots, and computing rank YouTube
  4. Matrix inverses and rank tests for linear systems YouTube
  5. Least-squares linear regression and normal equations YouTube
  6. Determinants, elimination, and invertibility YouTube
  7. Eigenvalues, eigenvectors, and the characteristic equation YouTube

Week 3

  1. Diagonalization using eigenvectors, matrix powers, and long-term behavior YouTube
  2. Symmetric matrices, spectral theorem, and orthogonal diagonalization YouTube
  3. Positive definite matrices, quadratic forms, Cholesky decomposition, and optimization YouTube
  4. Singular value decomposition: singular values, singular vectors, construction, and rank YouTube
  5. Principal component analysis: variance, covariance, projection, and dimensionality reduction YouTube
  6. PCA through SVD, low-rank approximation, image compression, and Eckart–Young theorem YouTube
  7. Random walks, Markov chains, stationary distributions, spectral mixing, and Monte Carlo simulation YouTube

Week 4

  1. Clustering, K-Means, and Introduction to Spectral Clustering YouTube
  2. Mathematical Reasoning for Spectral Clustering YouTube
  3. Complex Linear Algebra, Qubits, and Measurement YouTube
  4. Single-Qubit Gates: Actions and Examples YouTube
  5. Multi-Qubit States, Gates, and Density Matrices YouTube
  6. Separable States and Entanglement YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Indore
Department
Mathematics
Teacher
Prof. Ranveer Singh
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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