Sums and Products of Square-Zero Matrices |
| |
| Authors: | A Mohammadian |
| |
| Institution: | 1. School of Mathematics , Institute for Research in Fundamental Sciences (IPM) , Tehran , Iran ali_m@ipm.ir |
| |
| Abstract: | We show that for any two n × n square-zero matrices A and B over a division ring, if the right column spaces of AB and BA are the same, then the rank of AB is at most n/4, and if, in addition, the right null spaces of AB and BA are the same, then the rank of A + B is at most n/2. This generalizes some known results. |
| |
| Keywords: | Commutativity Matrices over division rings Nilpotent matrix Nullity Rank Square-zero matrix |
|
|
