Article ID Journal Published Year Pages File Type
4599108 Linear Algebra and its Applications 2015 12 Pages PDF
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 n≤4. They also proved that it is not true when n=5. We show that if rankJH≤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
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