The Structure of the Inverse to the Sylvester Resultant Matrix
| dc.creator | Lubachevsky, Boris D. | |
| dc.date | 2001-04-11 | |
| dc.date.accessioned | 2026-07-07T04:41:15Z | |
| dc.date.available | 2026-07-07T04:41:15Z | |
| dc.description | Given polynomials a(z) of degree m and b(z) of degree n, we represent the inverse to the Sylvester resultant matrix of a(z) and b(z), if this inverse exists, as a canonical sum of m+n dyadic matrices each of which is a rational function of zeros of a(z) and b(z). As a result, we obtain the polynomial solutions X(z) of degree n-1 and Y(z) of degree m-1 to the equation a(z)X(z)+b(z)Y(z)=c(z), where c(z) is a given polynomial of degree m+n-1, as follows: X(z) is a Lagrange interpolation polynomial for the function c(z)/a(z) over the set of zeros of b(z) and Y(z) is the one for the function c(z)/b(z) over the set of zeros of a(z). | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0104118 | |
| dc.identifier | http://arxiv.org/abs/math/0104118 | |
| dc.identifier | Linear Algebra and Its Applications 85:191-202 (1987) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61280 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 15A09; 15A06 | |
| dc.title | The Structure of the Inverse to the Sylvester Resultant Matrix | |
| dc.type | text |