Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416197 | Linear Algebra and its Applications | 2016 | 14 Pages |
Abstract
Let e1,â¦,ek be complex nÃn matrices such that eiej=âejei whenever iâ j. We conjecture that rk(e12)+rk(e22)+â¯+rk(ek2)â¤O(nlogâ¡n). We show that:(i).rk(e1n)+rk(e2n)+â¯+rk(ekn)â¤O(nlogâ¡n),(ii).if e12,â¦,ek2â 0 then kâ¤O(n),(iii).if e1,â¦,ek have full rank, or at least nâO(n/logâ¡n), then kâ¤O(logâ¡n). (i) implies that the conjecture holds if e12,â¦,ek2 are diagonalisable (or if e1,â¦,ek are). (ii) and (iii) show it holds when their rank is sufficiently large or sufficiently small.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Pavel Hrubeš,