The Binet-Cauchy Theorem for the Hyperdeterminant of boundary format multidimensional Matrices
| dc.creator | Dionisi, Carla | |
| dc.creator | Ottaviani, Giorgio | |
| dc.date | 2001-04-29 | |
| dc.date.accessioned | 2026-07-07T04:41:31Z | |
| dc.date.available | 2026-07-07T04:41:31Z | |
| dc.description | Let $A$, $B$ be multidimensional matrices of boundary format respectively $\prod_{i=0}^p(k_i+1)$, $\prod_{j=0}^q(l_j+1)$. Assume that $k_p=l_0$ so that the convolution $A\ast B$ is defined. We prove that $Det (A\ast B)=Det(A)^α\cdot Det(B)^β$ where $α= \frac {l_0!}{l_1!... l_q!}$, $β=\frac {(k_0+1)!}{k_1! ... k_{p-1}!(k_p+1)!}$ and $Det$ is the hyperdeterminant. When $A$, $B$ are square matrices this formula is the usual Binet-Cauchy Theorem computing the determinant of the product $A\cdot B$. It follows that $A \ast B$ is nondegenerate if and only if $A$ and $B$ are both nondegenerate. We show by a counterexample that the assumption of boundary format cannot be dropped. | |
| dc.description | LaTeX, 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0104281 | |
| dc.identifier | http://arxiv.org/abs/math/0104281 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61393 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Rings and Algebras | |
| dc.subject | 15A72; 14F05 | |
| dc.title | The Binet-Cauchy Theorem for the Hyperdeterminant of boundary format multidimensional Matrices | |
| dc.type | text |