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TATB10 Student presentations
Plan for 25-minute presentations using computer. A preliminary version (pdf) of the presentation must be handed in a few days before the time of the presentation.
Times for the presentations will be scheduled in TimeEdit.
Below follows a list of possible topics. You may also propose other topics.
Here the list of presentations 2026 with times, places and titles of presentations will be published (the list is updated during the course).
You may check the list of presentations 2010, 2013, 2015, 2017, 2020 and 2023. Note that these are for both the previous M.Sc. course TA1004 and the Ph.D. course 6FMAI14.
List of topics (section numbers refer to Horn and Johnson):
Topics indicated by * or ** have already been selected, but those with * are wider topics for which there is still room for more presentations.
Householder transformations
The QR algorithm
Lanczos tridiagonalization
Real Schur form and real spectral theorem for real normal matrices
Matrix groups
Graph Laplacians
Matrix completion
Markov chains
Random matrices
Numerical range / field of values
Hermitian similarity (Thm 4.1.7 & 3.2.3)
Prescribed interlacing eigenvalues (Thm 4.3.21)
Poincaré separation (4.3.28, 4.3.37)
Prescribed diagonal and eigenvalues (4.3.48)
Condition numbers (5.8)
Cauchy, Montel, Carmichael and Mason bounds on roots of polynomials (in exercises of 5.6)
Indicator matrices, irreducible matrices (6.2)
Ostrowski and Brauer theorems (6.4)
Approximation by unitary matrices (7.4.4-6)
Some singular value inequalities (exercise 7.3.P16 - more in Horn-Johnson II)
Total least squares
Lyapunov's theorem for stable matrices
Loewner partial order (7.7)
Structure of orthogonal matrices (6.5 in Treil)
Additive and multiplicative commutators (4.5 in Horn-Johnson II)
Angles between subspaces
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Senast uppdaterad: 2025-10-17