OS Reelle Geometrie und Algebra: Linear spaces of matrices of bounded rank

Freitag, 9. Juni 2023
13:30 bis 15 Uhr


Veranstaltet von
Mateusz Michalek

Vortragende Person/Vortragende Personen:
Joseph Landsberg

A classical problem in linear algebra is to determine the linear subspaces of the space of mxm matrices such that every matrix in the space has rank less than m. Let r be the maximum rank of a matrix in such a space. Such spaces were classified for r at most three in the 1980's but already for r=4, not only was there no classification, but no non-classical example of such a space was known. I will describe recent progress on this question. The progress uses tools from classical linear algebra, algebraic geometry and commutative algebra. As time permits, I will explain the motivations for this project from complexity theory and quantum information theory. This is joint work with Hang Huang.