Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416201 | Linear Algebra and its Applications | 2016 | 29 Pages |
Abstract
Fix a nonnegative integer d, a field F, and a vector space V over F with dimension d+1. Let T denote an invertible upper triangular matrix in Matd+1(F). Using T we construct three flags on V. We find a necessary and sufficient condition on T for these three flags to be totally opposite. In this case, we use these three totally opposite flags to construct a Billiard Array B on V. It is known that B is determined up to isomorphism by a certain triangular array of scalar parameters called the B-values. We compute these B-values in terms of the entries of T. We describe the set of isomorphism classes of Billiard Arrays in terms of upper triangular matrices.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yang Yang,