Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1311-9487-0 |
Объём: | 84 страниц |
Масса: | 147 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Given m and n and r < min(m, n), the determinantal variety Y r is the set of all m x n matrices (over a field k) with rank ? r. This is naturally an algebraic variety as the condition that a matrix have rank ? r is given by the vanishing of all of its (r + 1) x (r + 1) minors. Considering the generic m x n matrix whose entries are algebraically independent variables x i,j, these minors are polynomials of degree r + 1. The ideal of k[x i,j] generated by these polynomials is a determinantal ideal. Since the equations defining minors are homogeneous, one can consider Y r either as an affine variety in mn-dimensional affine space, or as a projective variety in (mn ? 1)-dimensional projective space.
Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.