Course - Numerical Linear Algebra MT25

Created: October 09, 2025 | Updated: December 04, 2025 | About these notes

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• Course webpage (old)
• Lecture notes
• Lecture slides
• Lecture recordings
  • 2024-2025
  • 2025-2026
• My notes here are based on the lecture notes and slides above, written by the course lecturer Prof. Yuji Nakatsukasa.
• Other courses this term: [[Courses MT25]]^U

Notes

• [[Notes - NLA MT25, Structured matrices]]^U
• [[Notes - NLA MT25, Vector and matrix norms]]^U
• [[Notes - NLA MT25, Subspaces]]^U
• [[Notes - NLA MT25, Singular value decomposition]]^U
• [[Notes - NLA MT25, Courant-Fischer minmax theorem]]^U
• [[Notes - NLA MT25, Weyl’s inequality]]^U
• [[Notes - NLA MT25, LU factorisation]]^U
• [[Notes - NLA MT25, Cholesky factorisation]]^U
• [[Notes - NLA MT25, QR factorisation]]^U
• [[Notes - NLA MT25, Linear systems]]^U
• [[Notes - NLA MT25, Least-squares]]^U
• [[Notes - NLA MT25, Numerical stability]]^U
• [[Notes - NLA MT25, Eigenvalue problems]]^U
• [[Notes - NLA MT25, Schur decomposition]]^U
• [[Notes - NLA MT25, Power method]]^U
• [[Notes - NLA MT25, QR algorithm]]^U
• [[Notes - NLA MT25, Krylov subspace methods]]^U
• [[Notes - NLA MT25, Arnoldi iteration]]^U
• [[Notes - NLA MT25, GMRES algorithm]]^U
• [[Notes - NLA MT25, Lanczos iteration]]^U
• [[Notes - NLA MT25, Conjugate gradient method]]^U
• [[Notes - NLA MT25, Chebyshev polynomials]]^U
• [[Notes - NLA MT25, Lanczos algorithm]]^U
• [[Notes - NLA MT25, Gaussian random matrices]]^U
• [[Notes - NLA MT25, Marchenko-Pastur theorem]]^U
• [[Notes - NLA MT25, Randomised least-squares]]^U
• [[Notes - NLA MT25, Useful miscellany]]^U

Related notes

There is a significant amount of overlap with the Part A [[Course - Numerical Analysis HT24]]^U, even some of the problem sheet questions are the same.

• [[Notes - Numerical Analysis HT24, Flops]]^U
• [[Notes - Numerical Analysis HT24, Singular value decomposition]]^U
• [[Notes - Numerical Analysis HT24, QR factorisation]]^U
• [[Notes - Numerical Analysis HT24, LU factorisation and Gaussian elimination]]^U
• [[Notes - Numerical Analysis HT24, Schur decomposition]]^U
• [[Notes - Numerical Analysis HT24, Power method]]^U
• [[Notes - Numerical Analysis HT24, Givens rotations]]^U
• [[Notes - Numerical Analysis HT24, Householder reflectors]]^U
• [[Notes - Numerical Analysis HT24, Eigenvalue problems]]^U
• [[Notes - Numerical Analysis HT24, Best approximation in inner product spaces]]^U

And some other relevant notes:

• [[Notes - Linear Algebra MT23, Jordan normal form]]^U
• [[Notes - Machine Learning MT23, Singular value decomposition]]^U
• [[Notes - Optimisation for Data Science HT25, Useful miscellany]]^U (some)

Problem Sheets

• Sheet 1 (old), solutions to A&C, [[Problem Sheet - NLA MT25, I]]^?
• Sheet 2 (old), solutions to A&C, solutions to B, [[Problem Sheet - NLA MT25, II]]^?
• Sheet 3 (old), solutions to A&C, [[Problem Sheet - NLA MT25, III]]^?
• Sheet 4 (old), code, solutions to A&C, solutions to B, [[Problem Sheet - NLA MT25, IV]]^? (changed slightly)

To-Do List

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Related posts

• [[Courses MT25]]^U

  (incoming)
• [[Part C]]^U

  (incoming)
• [[University Notes]]^U

  (incoming)
• [[Course - Probability MT25]]^U

  (sim: 0.712)
• [[Course - Geometric Deep Learning HT26]]^U

  (sim: 0.7)
• [[Course - Computer Vision MT25]]^U

  (sim: 0.662)
• [[Notes - NLA MT25, Randomised least-squares]]^U

  (incoming)
• [[Notes - NLA MT25, Marchenko-Pastur theorem]]^U

  (incoming)
• [[Notes - NLA MT25, Lanczos algorithm]]^U

  (incoming)
• [[Notes - NLA MT25, Cholesky factorisation]]^U

  (incoming)
• [[Notes - NLA MT25, QR algorithm]]^U

  (incoming)
• [[Notes - NLA MT25, Weyl's inequality]]^U

  (incoming)
• [[Notes - NLA MT25, Singular value decomposition]]^U

  (incoming)
• [[Notes - NLA MT25, LU factorisation]]^U

  (incoming)
• [[Notes - NLA MT25, Vector and matrix norms]]^U

  (incoming)
• [[Notes - NLA MT25, Numerical stability]]^U

  (incoming)
• [[Notes - NLA MT25, Useful miscellany]]^U

  (incoming)
• [[Notes - NLA MT25, Chebyshev polynomials]]^U

  (incoming)
• [[Notes - NLA MT25, Krylov subspace methods]]^U

  (incoming)
• [[Notes - NLA MT25, Gaussian random matrices]]^U

  (incoming)
• [[Notes - NLA MT25, Courant-Fischer minmax theorem]]^U

  (incoming)
• [[Notes - NLA MT25, Arnoldi iteration]]^U

  (incoming)
• [[Notes - NLA MT25, Linear systems]]^U

  (incoming)
• [[Notes - NLA MT25, QR factorisation]]^U

  (incoming)
• [[Notes - NLA MT25, Schur decomposition]]^U

  (incoming)
• [[Notes - NLA MT25, Subspaces]]^U

  (incoming)
• [[Notes - NLA MT25, GMRES algorithm]]^U

  (incoming)
• [[Notes - NLA MT25, Conjugate gradient method]]^U

  (incoming)
• [[Notes - NLA MT25, Power method]]^U

  (incoming)
• [[Notes - NLA MT25, Least-squares]]^U

  (incoming)
• [[Notes - NLA MT25, Eigenvalue problems]]^U

  (incoming)
• [[Notes - NLA MT25, Structured matrices]]^U

  (incoming)
• [[Notes - NLA MT25, Eigenvalue decomposition]]^U

  (incoming)
• [[Notes - NLA MT25, Lanczos iteration]]^U

  (incoming)
• [[Course - Linear Algebra I MT22]]^U

  (sim: 0.633)