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MAI0098 Student presentations

The examination consists of two parts, hand-in exercises and oral presentations. The exercises are to be solved individually. Ph.D. students need two oral presentations, undergraduate/M.Sc. students need one or two (check under examination on the course information page).

Plan for 25-minute presentations using OH/computer. A preliminary version of the presentation must be handed in a few days before the time of the presentation.

The first presentation should be before November 13, 2020.

Below follows a list of possible topics. You may also propose other topics. Topics related to your research are especially welcome.

Here is the list of presentations 2017 with times, places and titles of presentations (the list is updated during the course). 

You may check the list of presentations 2010, 2013
and 2015.

List of topics (section numbers refer to Horn and Johnson):

Topics indicated by ** have already been selected.

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 and Lagrange interpolation)
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: 2020-09-16