Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599108 | Linear Algebra and its Applications | 2015 | 12 Pages |
Abstract
Let H be a quadratic homogeneous polynomial map of dimension n over an infinite field in which 2 is invertible such that its Jacobian JH is nilpotent. Meisters and Olech have shown that JH is strongly nilpotent if nâ¤4. They also proved that it is not true when n=5. We show that if rankJHâ¤2 and n arbitrary, then JH is strongly nilpotent. We also give examples to show that this is no longer true for any rank and dimension as long as the rank is greater than 2.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kevin Pate, Charles Ching-An Cheng,