Abstract
In order to understand the triple action of PGLn+1 on the projective space of nonzero (n + 1) × (n + 1) matrices of linear forms on Pn, we associate a quadratic rational map φ{symbol} : Pn → Pn to any such matrix A. The properties of the dynamical system obtained by iteration of φ{symbol}, some of which are of a geometric nature, generate invariants and a canonical form for the orbit of A. We study a family of matrices parametrized by P1, whose associated geometry is given by the rational normal curve for each dimension n = 2, 3, 4. Our analysis involves the osculating flags to the curves; and we calculate the stabilizers of our rational maps and matrices.
Original language | English |
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Pages (from-to) | 363-379 |
Number of pages | 17 |
Journal | Linear Algebra and Its Applications |
Volume | 418 |
Issue number | 2-3 |
DOIs | |
State | Published - 15 Oct 2006 |
Keywords
- Canonical form
- Dynamical system
- Invariant
- Matrix of linear forms
- Osculating flag
- Polynomial identity
- Rational map
- Rational normal quartic
- Trilinear algebra
- Twisted cubic