Speaker
Geir Dahl
Description
We introduce a new rank concept for $(0,\pm 1)$-matrices, called the $\pm$-rank of a $(0,\pm 1)$-matrix. This ``generalizes'' the binary rank and the term rank of (0,1)-matrices. We establish several inequalities relating the different ranks, including ordinary real rank. Moreover, the $\pm$-rank is discussed for certain classes of $(0,\pm 1)$-matrices, such as alternating sign matrices (ASMs), network matrices etc. We also focus on some challenging problems concerning this rank concept, both of theoretical and computationally nature.
Authors
Geir Dahl
Prof.
Richard Brualdi
(University of Wisconsin)