Course - Numerical Linear Algebra MT25
- Course webpage (old)
- Lecture notes
- Lecture slides
- Lecture recordings
- 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, 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, 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]]? (changed slightly)
- Sheet 4 (old), code, solutions to A&C, solutions to B, [[Problem Sheet - NLA MT25, IV]]? (changed slightly)
To-Do List
- proofs of those useful norm inequalities
- proofs of all those properties of the SVD in lecture 3
- check whether “subordinate” is the correct term for $ \vert \vert AB \vert \vert _ p \le \vert \vert A \vert \vert _ p \vert \vert B \vert \vert _ p$, or if it should be “submultiplicative”