# Course - Numerical Linear Algebra MT25

> Source: https://ollybritton.com/notes/uni/part-c/mt25/nla/numerical-linear-algebra/ · Updated: 2026-05-18 · Tags: uni, course

- [Course webpage](https://courses.maths.ox.ac.uk/course/view.php?id=6110) ([old](https://courses.maths.ox.ac.uk/course/view.php?id=5563))
- [Lecture notes](https://courses.maths.ox.ac.uk/pluginfile.php/118397/mod_resource/content/35/NLA_lecture_notes.pdf)
- [Lecture slides](https://courses.maths.ox.ac.uk/pluginfile.php/118402/mod_resource/content/17/NLA_slides.pdf)
- Lecture recordings
	- [2024-2025](https://ox.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?embedded=1#folderID=%2205c6777b-df20-49cd-a0a3-b1b900989af8%22)****
	- [2025-2026](https://ox.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?embedded=1#folderID=%22c1ddf29a-0a3f-4e51-984b-b31a0079208c%22)
- My notes here are based on the lecture notes and slides above, written by the course lecturer [Prof. Yuji Nakatsukasa](https://people.maths.ox.ac.uk/nakatsukasa/).
- Other courses this term: [Courses MT25](https://ollybritton.com/notes/uni/part-a/mt25/)

### Notes
- [Notes - NLA MT25, Overview of results and methods](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/overview-of-results-and-methods/)

- [Notes - NLA MT25, Structured matrices](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/structured-matrices/)
- [Notes - NLA MT25, Vector and matrix norms](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/vector-and-matrix-norms/)
- [Notes - NLA MT25, Subspaces](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/subspaces/)
- [Notes - NLA MT25, Singular value decomposition](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/singular-value-decomposition/)
- [Notes - NLA MT25, Pseudoinverses](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/pseudoinverses/)
- [Notes - NLA MT25, Courant-Fischer minmax theorem](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/courant-fischer-minmax-theorem/)
- [Notes - NLA MT25, Weyl's inequality](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/weyls-inequality/)
- [Notes - NLA MT25, LU factorisation](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/lu-factorisation/)
- [Notes - NLA MT25, Cholesky factorisation](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/cholesky-factorisation/)
- [Notes - NLA MT25, QR factorisation](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/qr-factorisation/)
- [Notes - NLA MT25, Givens rotations](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/givens-rotations/)
- [Notes - NLA MT25, Linear systems](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/linear-systems/)
- [Notes - NLA MT25, Least-squares](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/least-squares/)
- [Notes - NLA MT25, Numerical stability](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/numerical-stability/)
- [Notes - NLA MT25, Eigenvalue problems](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/eigenvalue-problems/)
- [Notes - NLA MT25, Schur decomposition](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/schur-decomposition/)
- [Notes - NLA MT25, Power method](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/power-method/)
- [Notes - NLA MT25, QR algorithm](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/qr-algorithm/)
- [Notes - NLA MT25, Krylov subspace methods](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/krylov-subspace-methods/)
- [Notes - NLA MT25, Arnoldi decomposition and iteration](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/arnoldi-decomposition-and-iteration/)
- [Notes - NLA MT25, GMRES algorithm](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/gmres-algorithm/)
- [Notes - NLA MT25, Lanczos decomposition and iteration](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/lanczos-decomposition-and-iteration/)
- [Notes - NLA MT25, Conjugate gradient method](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/conjugate-gradient-method/)
- [Notes - NLA MT25, Chebyshev polynomials](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/chebyshev-polynomials/)
- [Notes - NLA MT25, Rayleigh-Ritz algorithm](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/rayleigh-ritz-algorithm/)
- [Notes - NLA MT25, Lanczos algorithm](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/lanczos-algorithm/)
- [Notes - NLA MT25, Gaussian random matrices](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/gaussian-random-matrices/)
- [Notes - NLA MT25, Marchenko-Pastur theorem](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/marchenko-pastur-theorem/)
- [Notes - NLA MT25, Randomised least-squares](https://ollybritton.com/notes/uni/part-c/mt25/nla/randomised-least-squares/)
- [Notes - NLA MT25, HMT algorithm](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/hmt-algorithm/)
- [Notes - NLA MT25, CUR approximation](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/cur-approximation/)
- [Notes - NLA MT25, Useful miscellany](https://ollybritton.com/notes/uni/part-c/mt25/nla/notes/useful-miscellany/)

### Related notes
There is a significant amount of overlap with the Part A [Course - Numerical Analysis HT24](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/), even some of the problem sheet questions are the same.

- [Notes - Numerical Analysis HT24, Misc](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/misc/)
- [Notes - Numerical Analysis HT24, Singular value decomposition](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/singular-value-decomposition/)
- [Notes - Numerical Analysis HT24, QR decomposition](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/qr-decomposition/)
- [Notes - Numerical Analysis HT24, LU decomposition](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/lu-decomposition/)
- [Notes - Numerical Analysis HT24, Schur decomposition](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/schur-decomposition/)
- [Notes - Numerical Analysis HT24, Power method](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/power-method/)
- [Notes - Numerical Analysis HT24, Givens rotations](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/givens-rotations/)
- [Notes - Numerical Analysis HT24, Householder reflectors](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/householder-reflectors/)
- [Notes - Numerical Analysis HT24, Eigenvalues](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/eigenvalues/)
- [Notes - Numerical Analysis HT24, Best approximation in inner product spaces](https://ollybritton.com/notes/uni/part-a/ht24/numerical-analysis/notes/best-approximation-in-inner-product-spaces/)

And some other relevant notes:

- [Notes - Linear Algebra MT23, Jordan normal form](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/jordan-normal-form/)
- [Notes - Machine Learning MT23, Singular value decomposition](https://ollybritton.com/notes/uni/part-a/mt23/machine-learning/notes/singular-value-decomposition/)
- [Notes - Optimisation for Data Science HT25, Misc](https://ollybritton.com/notes/uni/part-b/ht25/optimisation-for-data-science/notes/misc/) (some)

### Problem Sheets
- [Sheet 1 (old)](https://courses.maths.ox.ac.uk/pluginfile.php/105966/mod_assign/introattachment/0/sheet1.pdf), [solutions to A&C](https://courses.maths.ox.ac.uk/pluginfile.php/105966/mod_assign/introattachment/0/sheet1_solAC.pdf), [redacted](https://ollybritton.com/404)
- [Sheet 2 (old)](https://courses.maths.ox.ac.uk/pluginfile.php/105967/mod_assign/introattachment/0/sheet2.pdf), [solutions to A&C](https://courses.maths.ox.ac.uk/pluginfile.php/105967/mod_assign/introattachment/0/sheet2_solAC.pdf), [solutions to B](https://courses.maths.ox.ac.uk/pluginfile.php/105967/mod_assign/introattachment/0/sheet2_sol.pdf), [redacted](https://ollybritton.com/404)
- [Sheet 3 (old)](https://courses.maths.ox.ac.uk/pluginfile.php/105968/mod_assign/introattachment/0/sheet3.pdf), [solutions to A&C](https://courses.maths.ox.ac.uk/pluginfile.php/105968/mod_assign/introattachment/0/sheet3_solAC.pdf?forcedownload=1), [redacted](https://ollybritton.com/404)
- [Sheet 4 (old)](https://courses.maths.ox.ac.uk/pluginfile.php/105969/mod_assign/introattachment/0/sheet4.pdf), [code](https://courses.maths.ox.ac.uk/pluginfile.php/105969/mod_assign/introattachment/0/code_sheet4.m), [solutions to A&C](https://courses.maths.ox.ac.uk/pluginfile.php/105969/mod_assign/introattachment/0/sheet4_solAC.pdf), [solutions to B](https://courses.maths.ox.ac.uk/pluginfile.php/105969/mod_assign/introattachment/0/sheet4_sol.pdf), [redacted](https://ollybritton.com/404) (changed slightly)

### To-Do List

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