Speaker: Thomas Karam 副教授，上海交通大学

Inviter: 郭赫

Title: A min-max principle for matrix and tensor completion

Language: English

Time & Venue: 2026.10.13 14:00-15:00 N620

Abstract: It is known that the lowest rank arising from changing the diagonal entries of a matrix and the highest rank arising from restricting the matrix to an off-diagonal submatrix are in a sense two sides of the same coin, as they stand within a multiplicative factor of at most 3. Our focus in this talk shall be twofold.

First, we shall study how the above min-max principle can be extended to more general sets of modifiable matrix entries than the diagonal. If U is a set of entries, then does the highest rank of U-avoiding submatrices control the lowest rank of the matrix after modification of entries in U? As stated, this is far from being true uniformly over all sets U, but there is an adequate formulation that accounts for the complexity of U, in a sense made precise.

Second, we shall study the extension of this principle to the various rank notions on tensors that can be built from partitioning the coordinates. After recalling a known generalisation to the ranks of tensors of the matrix min-max principle with respect to the diagonal, we will examine increasingly general classes of sets of modifiable tensor entries.