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6FMAI14 Student presentations
Plan for 25-minute presentations using computer. A preliminary version of the presentation must be handed in a few days before the time of the presentation.
It is recommended that the first presentation is before October 16, 2023.
The second presentation must be before November 29, 2023.
Below follows a list of possible topics. You may also propose other topics. Topics related to your research are especially welcome, all Ph.D. students are strongly encouraged to choose such topics.
Here is the list of presentations 2023 with times, places and titles of presentations (the list is updated during the course).
You may check the list of presentations 2010, 2013, 2015, 2017 and 2020.
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
Sidansvarig: goran.bergqvist@liu.se
Senast uppdaterad: 2023-11-24