Course - Numerical Linear Algebra MT25

Created: October 09, 2025 | Updated: May 18, 2026 | Read markdown | About these notes

---

• 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, Overview of results and methods^U

• 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, Pseudoinverses^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, Givens rotations^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 decomposition and iteration^U
• Notes - NLA MT25, GMRES algorithm^U
• Notes - NLA MT25, Lanczos decomposition and iteration^U
• Notes - NLA MT25, Conjugate gradient method^U
• Notes - NLA MT25, Chebyshev polynomials^U
• Notes - NLA MT25, Rayleigh-Ritz algorithm^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, HMT algorithm^U
• Notes - NLA MT25, CUR approximation^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, Misc^U
• Notes - Numerical Analysis HT24, Singular value decomposition^U
• Notes - Numerical Analysis HT24, QR decomposition^U
• Notes - Numerical Analysis HT24, LU decomposition^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, Eigenvalues^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, Misc^U (some)

Problem Sheets

• Sheet 1 (old), solutions to A&C, redacted^?
• Sheet 2 (old), solutions to A&C, solutions to B, redacted^?
• Sheet 3 (old), solutions to A&C, redacted^?
• Sheet 4 (old), code, solutions to A&C, solutions to B, redacted^? (changed slightly)

To-Do List

---

Related posts

• Notes - NLA MT25, Randomised least-squares^U

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  (incoming)
• Notes - NLA MT25, Pseudoinverses^U

  (incoming)
• Notes - NLA MT25, Lanczos decomposition and iteration^U

  (incoming)
• Notes - NLA MT25, Arnoldi decomposition and iteration^U

  (incoming)
• Notes - NLA MT25, CUR approximation^U

  (incoming)
• Notes - NLA MT25, HMT algorithm^U

  (incoming)
• Notes - NLA MT25, Rayleigh-Ritz algorithm^U

  (incoming)
• Notes - NLA MT25, Overview of results and methods^U

  (incoming)
• Notes - NLA MT25, Givens rotations^U

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

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

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

  (incoming)
• Part C^U

  (incoming)
• University Notes^U

  (incoming)
• Courses MT25^U

  (incoming)
• Course - Probability MT25^U

  (sim: 0.627)
• Course - Linear Algebra MT23^U

  (sim: 0.647)
• Course - Geometric Deep Learning HT26^U

  (sim: 0.637)
• Course - Linear Algebra MT22^U

  (sim: 0.627)