Math 2.0

Resources / course

Linear Algebra for Machine Learning and Quantum Computing 94FSD3H3SX

URIm2://res/94FSD3H3SX
Kindcourse
CreatorsRanveer Singh (instructor)
Date2026-08-09
Scopein

Expressions

e1: edition

Languageen
Date2026-08-09
Contents
  • part 1: Week 1
  • session 1: Matrix product as linear combinations
  • session 2: Linear dependence and bases
  • session 3: Inner products and projections
  • session 4: Projection onto subspaces and projection matrices
  • session 5: Least squares problems, reflections, rotations
  • session 6: Gram-Schmidt orthogonalization and QR decomposition
  • part 2: Week 2
  • session 7: Four fundamental subspaces and their orthogonality
  • session 8: Matrix rank and the rank-nullity theorem
  • session 9: Gaussian elimination, pivots, and computing rank
  • session 10: Matrix inverses and rank tests for linear systems
  • session 11: Least-squares linear regression and normal equations
  • session 12: Determinants, elimination, and invertibility
  • session 13: Eigenvalues, eigenvectors, and the characteristic equation
  • part 3: Week 3
  • session 14: Diagonalization using eigenvectors, matrix powers, and long-term behavior
  • session 15: Symmetric matrices, spectral theorem, and orthogonal diagonalization
  • session 16: Positive definite matrices, quadratic forms, Cholesky decomposition, and optimization
  • session 17: Singular value decomposition: singular values, singular vectors, construction, and rank
  • session 18: Principal component analysis: variance, covariance, projection, and dimensionality reduction
  • session 19: PCA through SVD, low-rank approximation, image compression, and Eckart–Young theorem
  • session 20: Random walks, Markov chains, stationary distributions, spectral mixing, and Monte Carlo simulation
  • part 4: Week 4
  • session 21: Clustering, K-Means, and Introduction to Spectral Clustering
  • session 22: Mathematical Reasoning for Spectral Clustering
  • session 23: Complex Linear Algebra, Qubits, and Measurement
  • session 24: Single-Qubit Gates: Actions and Examples
  • session 25: Multi-Qubit States, Gates, and Density Matrices
  • session 26: Separable States and Entanglement

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